{"id":14646,"date":"2021-05-20T18:46:27","date_gmt":"2021-05-20T13:16:27","guid":{"rendered":"https:\/\/learnsteer.sasnaka.org\/science\/?p=14646"},"modified":"2022-01-27T01:53:49","modified_gmt":"2022-01-26T20:23:49","slug":"01-04-00","status":"publish","type":"post","link":"https:\/\/learnsteer.sasnaka.org\/science\/advanced-level-science\/01-04-00\/","title":{"rendered":"01.04.00- \u0dad\u0dca\u200d\u0dbb\u0dd2\u0d9a\u0ddd\u0dab\u0db8\u0dd2\u0dad\u0dd2\u0d9a \u0dc3\u0dbb\u0dca\u0dc0\u0dc3\u0dcf\u0db8\u0dca\u200d\u0dba"},"content":{"rendered":"\r\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-block-buttons-is-layout-flex\">\r\n<div class=\"wp-block-button is-style-shadow\"><a class=\"wp-block-button__link\" style=\"border-radius: 15px\" href=\"https:\/\/drive.google.com\/uc?export=download&amp;id=1uREA7gQugv5oy0w1di6xEwEAL_2sGNSR\" target=\"_blank\" rel=\"noreferrer noopener\">\u0db4\u0dcf\u0da9\u0db8\u0dda \u0dc3\u0da7\u0dc4\u0db1 Download \u0d9a\u0dbb\u0d9c\u0db1\u0dca\u0db1.<\/a><\/div>\r\n<\/div>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li><strong><span class=\"has-inline-color\" style=\"color: #ff0000\">\u0dc3\u0d82\u0dba\u0dd4\u0d9a\u0dca\u0dad \u0d9c\u0dab\u0dd2\u0dad\u0dba 1 (\u0dc1\u0dd4\u0daf\u0dca\u0db0 \u0d9c\u0dab\u0dd2\u0dad\u0dba )\u0db4\u0dca\u200d\u0dbb\u0dc1\u0dca\u0db1 \u0db4\u0dad\u0dca\u200d\u0dbb\u0dba\u0dda A \u0d9a\u0ddc\u0da7\u0dc3\u0dda (\u0d9a\u0dd9\u0da7\u0dd2 \u0db4\u0dca\u200d\u0dbb\u0dc1\u0dca\u0db1 ) 10 \u0dc0\u0dd0\u0db1\u0dd2 \u0d9c\u0dd0\u0da7\u0dc5\u0dd4\u0dc0\u0dda \u0dc4\u0dcf B \u0d9a\u0ddc\u0da7\u0dc3\u0dda (\u0dbb\u0da0\u0db1\u0dcf \u0db4\u0dca\u200d\u0dbb\u0dc1\u0dca\u0db1 )17 \u0d9c\u0dd0\u0da7\u0dc5\u0dd4\u0dc0\u0dda \u0d85\u0da9\u0d82\u0d9c\u0dd4 \u0dc0\u0db1\u0dca\u0db1\u0dda \u0db8\u0dd9\u0db8 \u0db4\u0dcf\u0da9\u0db8\u0dda \u0d85\u0da9\u0d82\u0d9c\u0dd4 \u0dc3\u0dd2\u0daf\u0dca\u0db0\u0dcf\u0db1\u0dca\u0dad \u0dc0\u0dda.<\/span><\/strong><\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<h2 class=\"wp-block-heading\"><strong>\u0dad\u0dca\u200d\u0dbb\u0dd2\u0d9a\u0ddd\u0dab\u0db8\u0dd2\u0dad\u0dd2\u0d9a<\/strong> <strong>\u0db4\u0dca\u200d\u0dbb\u0db0\u0dcf\u0db1 \u0dc3\u0dbb\u0dca\u0dc0\u0dc3\u0dcf\u0db8\u0dca\u200d\u0dba<\/strong><\/h2>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-31603 \" src=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/Pasted-into-01.04.00-\u0dad\u0dca\u200d\u0dbb\u0dd2\u0d9a\u0ddd\u0dab\u0db8\u0dd2\u0dad\u0dd2\u0d9a-\u0dc3\u0dbb\u0dca\u0dc0\u0dc3\u0dcf\u0db8\u0dca\u200d\u0dba.png\" width=\"444\" height=\"354\" srcset=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/Pasted-into-01.04.00-\u0dad\u0dca\u200d\u0dbb\u0dd2\u0d9a\u0ddd\u0dab\u0db8\u0dd2\u0dad\u0dd2\u0d9a-\u0dc3\u0dbb\u0dca\u0dc0\u0dc3\u0dcf\u0db8\u0dca\u200d\u0dba.png 569w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/Pasted-into-01.04.00-\u0dad\u0dca\u200d\u0dbb\u0dd2\u0d9a\u0ddd\u0dab\u0db8\u0dd2\u0dad\u0dd2\u0d9a-\u0dc3\u0dbb\u0dca\u0dc0\u0dc3\u0dcf\u0db8\u0dca\u200d\u0dba-300x239.png 300w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/Pasted-into-01.04.00-\u0dad\u0dca\u200d\u0dbb\u0dd2\u0d9a\u0ddd\u0dab\u0db8\u0dd2\u0dad\u0dd2\u0d9a-\u0dc3\u0dbb\u0dca\u0dc0\u0dc3\u0dcf\u0db8\u0dca\u200d\u0dba-150x120.png 150w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/Pasted-into-01.04.00-\u0dad\u0dca\u200d\u0dbb\u0dd2\u0d9a\u0ddd\u0dab\u0db8\u0dd2\u0dad\u0dd2\u0d9a-\u0dc3\u0dbb\u0dca\u0dc0\u0dc3\u0dcf\u0db8\u0dca\u200d\u0dba-526x420.png 526w\" sizes=\"(max-width: 444px) 100vw, 444px\" \/><\/p>\r\n\r\n\r\n\r\n\r\n\r\n<p>ABC \u0dba\u0db1\u0dd4 \u0dc3\u0dd8\u0da2\u0dd4\u0d9a\u0ddd\u0dab\u0dd2 \u0dad\u0dca\u200d\u0dbb\u0dd2\u0d9a\u0ddd\u0dab\u0dba\u0d9a\u0dd2. <span class=\"wp-katex-eq\" data-display=\"false\">C\\widehat AB=\\theta<\/span>\u0dc0\u0dda.<\/p>\r\n\r\n\r\n\r\n<p><span class=\"wp-katex-eq\" data-display=\"false\">\\cos\\;\\theta=\\frac{AB}{AC}<\/span> \u0dc4\u0dcf <span class=\"wp-katex-eq\" data-display=\"false\">\\sin\\;\\theta=\\frac{BC}{AC}<\/span> \u0dc0\u0dda.<\/p>\r\n\r\n\r\n\r\n<p>\u0db4\u0dba\u0dd2\u0dad\u0d9c\u0dbb\u0dc3\u0dca \u0db4\u0dca\u200d\u0dbb\u0db8\u0dda\u0dba\u0dba\u0da7 \u0d85\u0db1\u0dd4\u0dc0,<\/p>\r\n\r\n\r\n\r\n<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}AB^2+BC^2&amp;=&amp;AC^2\\\\&amp;&amp;\\\\\\frac{AB^2}{AC^2}+\\frac{BC^2}{AC^2}&amp;=&amp;\\frac{AC^2}{AC^2}\\\\&amp;&amp;\\\\\\left(\\frac{AB}{AC}\\right)^2+\\left(\\frac{BC}{AC}\\right)^2&amp;=&amp;1\\end{array}<\/span>\r\n\r\n\r\n\r\n<div class=\"wp-block-spacer\" style=\"height: 36px\" aria-hidden=\"true\">\u00a0<\/div>\r\n\r\n\r\n\r\n<p class=\"has-text-align-left\"><span class=\"has-inline-color\" style=\"color: #ff0000\">Cos<sup>2<\/sup><span class=\"wp-katex-eq\" data-display=\"false\">\\theta<\/span> + Sin<sup>2<\/sup><span class=\"wp-katex-eq\" data-display=\"false\">\\theta<\/span> = 1<\/span><\/p>\r\n\r\n\r\n\r\n<p>(\u03b8 \u0dc4\u0dd2 \u0d95\u0db1\u0dd1\u0db8 \u0d85\u0d9c\u0dba\u0d9a\u0da7 \u0dc3\u0dad\u0dca\u200d\u0dba \u0dc0\u0dda.)<\/p>\r\n\r\n\r\n\r\n<div class=\"wp-block-spacer\" style=\"height: 20px\" aria-hidden=\"true\">\u00a0<\/div>\r\n\r\n\r\n\r\n<p>Cos<sup>2<\/sup>\u03b8 + Sin<sup>2<\/sup>\u03b8 = 1<\/p>\r\n\r\n\r\n\r\n<p>Cos\u03b8 \u2260 0 \u0dc0\u0db1 \u0dc0\u0dd2\u0da7,<\/p>\r\n\r\n\r\n\r\n<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\\frac{C\\mathrm{os}^2\\theta}{C\\mathrm{os}^2\\theta}\\;+\\frac{Sin^2\\theta}{C\\mathrm{os}^2\\theta}&amp;=&amp;\\frac1{C\\mathrm{os}^2\\theta}\\\\&amp;&amp;\\\\1\\;+\\;\\left(\\frac{Sin\\;\\theta}{C\\mathrm{os}\\;\\theta}\\right)^2&amp;=&amp;\\left(\\frac1{C\\mathrm{os}\\;\\theta}\\right)^2\\\\&amp;&amp;\\\\1\\;+\\;\\left(\\tan\\;\\theta\\right)^2\\;&amp;=&amp;\\left(Sec\\;\\theta\\right)^2\\end{array}<\/span>\r\n\r\n\r\n\r\n<div class=\"wp-block-spacer\" style=\"height: 20px\" aria-hidden=\"true\">\u00a0<\/div>\r\n\r\n\r\n\r\n<p><span class=\"has-inline-color\" style=\"color: #ff0000\">Sec<sup>2<\/sup>\u03b8 = 1 + tan <sup>2<\/sup>\u03b8<\/span><\/p>\r\n\r\n\r\n\r\n<p>(Cos \u03b8 \u22600 \u0dc0\u0db1 \u0d95\u0db1\u0dd1\u0db8 \u0d85\u0d9c\u0dba\u0d9a\u0da7 \u0dc3\u0dad\u0dca\u200d\u0dba \u0dc0\u0dda.)<\/p>\r\n\r\n\r\n\r\n<div class=\"wp-block-spacer\" style=\"height: 19px\" aria-hidden=\"true\">\u00a0<\/div>\r\n\r\n\r\n\r\n<p>Cos<sup>2<\/sup>\u03b8 + Sin<sup>2<\/sup>\u03b8 = 1<\/p>\r\n\r\n\r\n\r\n<p>Sin\u03b8 \u2260 0 \u0dc0\u0db1 \u0dc0\u0dd2\u0da7.<\/p>\r\n\r\n\r\n\r\n<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\\frac{C\\mathrm{os}^2\\theta}{Sin^2\\theta}\\;+\\frac{Sin^2\\theta}{Sin^2\\theta}&amp;=&amp;\\frac1{Sin^2\\theta}\\\\&amp;&amp;\\\\1\\;+\\;\\left(\\frac{Cos\\;\\theta}{\\;Sin\\;\\theta}\\right)^2&amp;=&amp;\\left(\\frac1{Sin\\;\\theta}\\right)^2\\\\&amp;&amp;\\\\1\\;+\\;\\left(Cot\\;\\theta\\right)^2\\;&amp;=&amp;\\left(Cosec\\;\\theta\\right)^2\\end{array}<\/span>\r\n\r\n\r\n\r\n<div class=\"wp-block-spacer\" style=\"height: 34px\" aria-hidden=\"true\">\u00a0<\/div>\r\n\r\n\r\n\r\n<p><span class=\"has-inline-color\" style=\"color: #ff0000\">Cosec<sup>2<\/sup>\u03b8= 1 + cot<sup>2<\/sup>\u03b8<\/span><\/p>\r\n\r\n\r\n\r\n<p>(Sin \u03b8 \u22600 \u0dc0\u0db1 \u0d95\u0db1\u0dd1\u0db8 \u0d85\u0d9c\u0dba\u0d9a\u0da7 \u0dc3\u0dad\u0dca\u200d\u0dba \u0dc0\u0dda.)<\/p>\r\n\r\n\r\n\r\n<p>Cos<sup>2<\/sup>\u03b8 + Sin<sup>2<\/sup>\u03b8 = 1<\/p>\r\n\r\n\r\n\r\n<p>Sec<sup>2<\/sup>\u03b8 = 1 + tan <sup>2<\/sup>\u03b8<\/p>\r\n\r\n\r\n\r\n<p>Cosec<sup>2<\/sup>\u03b8 = 1 + Cot<sup>2<\/sup>\u03b8<\/p>\r\n\r\n\r\n\r\n<p>\u0d89\u0dc4\u0dad \u0db4\u0dca\u200d\u0dbb\u0d9a\u0dcf\u0dc1\u0db1\u0dc0\u0dbd\u0da7 \u0dad\u0dca\u200d\u0dbb\u0dd2\u0d9a\u0ddd\u0dab\u0db8\u0dd2\u0dad\u0dd2\u0d9a \u0db4\u0dca\u200d\u0dbb\u0db0\u0dcf\u0db1 \u0dc3\u0dbb\u0dca\u0dc0\u0dc3\u0dcf\u0db8\u0dca\u200d\u0dba \u0dba\u0dd0\u0dba\u0dd2 \u0d9a\u0dd2\u0dba\u0db1\u0dd4 \u0dbd\u0dd0\u0db6\u0dda.<\/p>\r\n\r\n\r\n\r\n<div class=\"wp-block-cover alignfull has-background-dim\" style=\"background-color: #eee2dc;min-height: 325px;aspect-ratio:unset;\">\r\n<div class=\"wp-block-cover__inner-container is-layout-flow wp-block-cover-is-layout-flow\">\r\n<p class=\"has-text-align-center has-text-color\" style=\"color: #123c69;font-size: 20px\">\u0d9a\u0ddd\u0dab\u0dba \u0d9a\u0dd3\u0dba\u0daf? (\u0dbb\u0dd6\u0db4\u0dba\u0dda \u0daf\u0d9a\u0dca\u0dc0\u0dcf \u0d87\u0dad\u0dca\u0dad\u0dda \u0db4\u0dcf\u0daf\u0dba\u0d9a\u0dca \u0d92\u0d9a\u0d9a 2 \u0d9a\u0dca \u0dc0\u0dd6 \u0dc3\u0db8\u0da0\u0dad\u0dd4\u0dbb\u0dc3\u0dca\u200d\u0dbb\u0dba\u0d9a\u0dd2.)<\/p>\r\n\r\n\r\n\r\n<div class=\"wp-block-image\">\r\n<figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-29815\" src=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/09\/imageonline-co-whitebackgroundremoved-3-2-1024x985.png\" alt=\"\" width=\"256\" height=\"246\" srcset=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/09\/imageonline-co-whitebackgroundremoved-3-2-1024x985.png 1024w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/09\/imageonline-co-whitebackgroundremoved-3-2-300x289.png 300w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/09\/imageonline-co-whitebackgroundremoved-3-2-768x739.png 768w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/09\/imageonline-co-whitebackgroundremoved-3-2-150x144.png 150w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/09\/imageonline-co-whitebackgroundremoved-3-2-696x669.png 696w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/09\/imageonline-co-whitebackgroundremoved-3-2-1068x1027.png 1068w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/09\/imageonline-co-whitebackgroundremoved-3-2-437x420.png 437w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/09\/imageonline-co-whitebackgroundremoved-3-2.png 1123w\" sizes=\"(max-width: 256px) 100vw, 256px\" \/><\/figure>\r\n<\/div>\r\n\r\n\r\n\r\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-block-buttons-is-layout-flex\">\r\n<div class=\"wp-block-button is-style-shadow\"><a class=\"wp-block-button__link has-text-color has-background\" style=\"border-radius: 10px;background: linear-gradient(135deg,#edc7b7 0%,#edc7b7 100%);color: #ce673b\" href=\"https:\/\/learnsteer.sasnaka.org\/science\/advanced-level-science\/combined-mathematics\/infinite-thinking\/01-04-00-q1\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u0db4\u0dd2\u0dc5\u0dd2\u0dad\u0dd4\u0dbb \u0db4\u0dd9\u0db1\u0dca\u0dc0\u0db1\u0dca\u0db1<\/a><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n\r\n\r\n\r\n<h4 class=\"wp-block-heading\"><span class=\"has-inline-color\" style=\"color: #304170\">\u0dad\u0dca\u200d\u0dbb\u0dd2\u0d9a\u0ddd\u0dab\u0db8\u0dd2\u0dad\u0dd2\u0d9a \u0dc3\u0dbb\u0dca\u0dc0\u0dc3\u0dcf\u0db8\u0dca\u200d\u0dba \u0dc3\u0dcf\u0db0\u0db1\u0dba \u0d9a\u0dd2\u0dbb\u0dd3\u0db8<\/span><\/h4>\r\n\r\n\r\n\r\n<p>A=B \u0dc3\u0dbb\u0dca\u0dc0\u0dc3\u0dcf\u0db8\u0dca\u200d\u0dba \u0dc3\u0dcf\u0db0\u0db1\u0dba \u0d9a\u0dd2\u0dbb\u0dd3\u0db8 \u0dc3\u0db3\u0dc4\u0dcf ,<\/p>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li>A \u0d9c\u0dd9\u0db1\u0dca \u0d86\u0dbb\u0db8\u0dca\u0db7 \u0d9a\u0dbb \u0d91\u0dba\u0da7 \u0d9c\u0dab\u0dd2\u0dad \u0d9a\u0dbb\u0dca\u0db8 \u0dba\u0ddc\u0daf\u0dcf \u0d91\u0dba B \u0da7 \u0dc3\u0db8\u0dcf\u0db1 \u0db6\u0dc0 \u0dc3\u0dcf\u0db0\u0db1\u0dba \u0d9a\u0dc5 \u0dc4\u0dd0\u0d9a.<\/li>\r\n<li>B \u0d9c\u0dd9\u0db1\u0dca \u0d86\u0dbb\u0db8\u0dca\u0db7 \u0d9a\u0dbb \u0d91\u0dba\u0da7 \u0d9c\u0dab\u0dd2\u0dad \u0d9a\u0dbb\u0dca\u0db8 \u0dba\u0ddc\u0daf\u0dcf \u0d91\u0dba A \u0da7 \u0dc3\u0db8\u0dcf\u0db1 \u0db6\u0dc0 \u0dc3\u0dcf\u0db0\u0db1\u0dba \u0d9a\u0dc5 \u0dc4\u0dd0\u0d9a.<\/li>\r\n<li>A\u0dad\u0dca B\u0dad\u0dca \u0db4\u0dca\u200d\u0dbb\u0d9a\u0dcf\u0dc1 \u0daf\u0dd9\u0d9a\u0db8 \u0dc0\u0dd9\u0db1\u0dad\u0dca C\u0db1\u0db8\u0dca \u0d91\u0d9a\u0db8 \u0db4\u0dca\u200d\u0dbb\u0d9a\u0dcf\u0dc1\u0db1\u0dba\u0d9a\u0da7 \u0dc3\u0db8\u0dcf\u0db1 \u0db6\u0dc0 \u0dc3\u0dcf\u0db0\u0db1\u0dba \u0d9a\u0dc5 \u0dc4\u0dd0\u0d9a.<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<p><strong>\u0d8b\u0daf\u0dcf:- (1.)Cos<\/strong><strong><sup>2<\/sup><\/strong><strong>A. tan<\/strong><strong><sup>2<\/sup><\/strong><strong>A + Sin<\/strong><strong><sup>2<\/sup><\/strong><strong>A. Cot<\/strong><strong><sup>2<\/sup><\/strong><strong>A<\/strong> <strong>=1 \u0db6\u0dc0 \u0db4\u0dd9\u0db1\u0dca\u0dc0\u0db1\u0dca\u0db1.<\/strong><\/p>\r\n\r\n\r\n\r\n<p>\u00a0 L.H.S = Cos<sup>2<\/sup>A. tan<sup>2<\/sup>A + Sin<sup>2<\/sup>A. Cot<sup>2<\/sup>A<\/p>\r\n\r\n\r\n\r\n<p>= Cos<sup>2<\/sup>A. (<span class=\"wp-katex-eq\" data-display=\"false\">\\frac{Sin^2A}{Cos^2A}<\/span>) + Sin<sup>2<\/sup>A. (<span class=\"wp-katex-eq\" data-display=\"false\">\\frac{Cos^2A}{Sin^2A}<\/span>)<\/p>\r\n\r\n\r\n\r\n<p>= Sin<sup>2<\/sup>A + Cos<sup>2<\/sup>A<\/p>\r\n\r\n\r\n\r\n<p>= 1<\/p>\r\n\r\n\r\n\r\n<p>= R.H.S<\/p>\r\n\r\n\r\n\r\n<p><strong>\u0d8b\u0daf\u0dcf:- (2.)<\/strong> <strong>tan<\/strong><strong><sup>2<\/sup><\/strong><strong>A + tan<\/strong><strong><sup>4<\/sup><\/strong><strong>A= Sec<\/strong><strong><sup>4<\/sup><\/strong><strong>A &#8211; Sec<\/strong><strong><sup>2<\/sup><\/strong><strong>A \u0db6\u0dc0 \u0db4\u0dd9\u0db1\u0dca\u0dc0\u0db1\u0dca\u0db1.<\/strong><\/p>\r\n\r\n\r\n\r\n<p>L.H.S = tan<sup>2<\/sup>A + tan<sup>4<\/sup>A<\/p>\r\n\r\n\r\n\r\n<p>= tan<sup>2<\/sup>A( 1 + tan<sup>2<\/sup>A)<\/p>\r\n\r\n\r\n\r\n<p>=( Sec<sup>2<\/sup>A \u2013 1).Sec<sup>2<\/sup>A<\/p>\r\n\r\n\r\n\r\n<p>= Sec<sup>4<\/sup>A &#8211; Sec<sup>2<\/sup>A<\/p>\r\n\r\n\r\n\r\n<p>= R.H.S<\/p>\r\n\r\n\r\n\r\n<p><strong>\u0d8b\u0daf\u0dcf:- (3.) (1- Cos<\/strong><strong><sup>2<\/sup><\/strong><strong>A).(1+ tan<\/strong><strong><sup>2<\/sup><\/strong><strong>A) = tan<\/strong><strong><sup>2<\/sup><\/strong><strong>A \u0db6\u0dc0 \u0db4\u0dd9\u0db1\u0dca\u0dc0\u0db1\u0dca\u0db1.<\/strong><\/p>\r\n\r\n\r\n\r\n<p>L.H.S = (1- Cos<sup>2<\/sup>A).(1+ tan<sup>2<\/sup>A)<\/p>\r\n\r\n\r\n\r\n<p>= Sin<sup>2<\/sup>A . Sec<sup>2<\/sup>A<\/p>\r\n\r\n\r\n\r\n<p>= Sin<sup>2<\/sup>A.(<span class=\"wp-katex-eq\" data-display=\"false\">\\frac1{Cos^2A}<\/span>)<\/p>\r\n\r\n\r\n\r\n<p>= tan<sup>2<\/sup>A<\/p>\r\n\r\n\r\n\r\n<p>= R.H.S<\/p>\r\n\r\n\r\n\r\n<p><strong>\u0d8b\u0daf\u0dcf:- (4.) (Sin <\/strong>\u03b8<strong> + Cos <\/strong>\u03b8<strong>).( 1 &#8211; Sin <\/strong>\u03b8.<strong>Cos <\/strong>\u03b8) = <strong>Sin<\/strong><strong><sup>3<\/sup><\/strong>\u03b8 + <strong>Cos<\/strong><strong><sup>3<\/sup><\/strong>\u03b8 <strong>\u0db6\u0dc0 \u0db4\u0dd9\u0db1\u0dca\u0dc0\u0db1\u0dca\u0db1.<\/strong><\/p>\r\n\r\n\r\n\r\n<p><strong>\u0d9a\u0dca\u200d\u0dbb\u0db8\u0dba 1<\/strong><\/p>\r\n\r\n\r\n\r\n<p>L.H.S = (Sin \u03b8 + Cos \u03b8).( 1 &#8211; Sin \u03b8.Cos \u03b8)<\/p>\r\n\r\n\r\n\r\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= Sin \u03b8- Sin<sup>2<\/sup>\u03b8. Cos \u03b8 + Cos\u03b8 &#8211; Sin \u03b8. Cos<sup>2<\/sup>\u03b8<\/p>\r\n\r\n\r\n\r\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= Sin \u03b8- Sin \u03b8. Cos<sup>2<\/sup>\u03b8 + Cos\u03b8- Sin<sup>2<\/sup>\u03b8. Cos \u03b8<\/p>\r\n\r\n\r\n\r\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= Sin \u03b8 (1- Cos<sup>2<\/sup>\u03b8) + Cos \u03b8(1- Sin<sup>2<\/sup>\u03b8)\u00a0<\/p>\r\n\r\n\r\n\r\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= Sin \u03b8. Sin<sup>2<\/sup>\u03b8 + Cos \u03b8.Cos<sup>2<\/sup>\u03b8<\/p>\r\n\r\n\r\n\r\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= Sin<sup>3<\/sup>\u03b8 + Cos<sup>3<\/sup>\u03b8<\/p>\r\n\r\n\r\n\r\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= R.H.S<\/p>\r\n\r\n\r\n\r\n<p><strong>\u0d9a\u0dca\u200d\u0dbb\u0db8\u0dba 2<\/strong><\/p>\r\n\r\n\r\n\r\n<p>L.H.S = (Sin \u03b8 + Cos \u03b8).( 1 &#8211; Sin \u03b8.Cos \u03b8)<\/p>\r\n\r\n\r\n\r\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= (Sin \u03b8 + Cos \u03b8).( Sin<sup>2<\/sup>\u03b8+ Cos<sup>2<\/sup>\u03b8- Sin\u03b8.Cos\u03b8)<\/p>\r\n\r\n\r\n\r\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= (Sin \u03b8 + Cos \u03b8).( Sin<sup>2<\/sup>\u03b8 &#8211; Sin\u03b8.Cos\u03b8+ Cos<sup>2<\/sup>\u03b8)<\/p>\r\n\r\n\r\n\r\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= Sin<sup>3<\/sup>\u03b8 + Cos<sup>3<\/sup>\u03b8<\/p>\r\n\r\n\r\n\r\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= R.H.S<\/p>\r\n\r\n\r\n\r\n<p><strong>\u0d8b\u0daf\u0dcf:- (5.) Cos <\/strong><strong><sup>6<\/sup><\/strong>\u03b8<strong> + Sin <\/strong><strong><sup>6<\/sup><\/strong>\u03b8<strong>\u00a0 = 1 \u2013 3 Sin<\/strong><strong><sup>2<\/sup><\/strong>\u03b8. <strong>Cos<\/strong><strong><sup>2<\/sup><\/strong>\u03b8<strong>\u00a0 \u0db6\u0dc0 \u0db4\u0dd9\u0db1\u0dca\u0dc0\u0db1\u0dca\u0db1.<\/strong><\/p>\r\n\r\n\r\n\r\n<p>L.H.S = Cos <sup>6<\/sup>\u03b8 + Sin <sup>6<\/sup>\u03b8\u00a0\u00a0<\/p>\r\n\r\n\r\n\r\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= (Cos<sup>2<\/sup>\u03b8)<sup>3 <\/sup>+ (Sin<sup>2<\/sup>\u03b8)<sup>3<\/sup><\/p>\r\n\r\n\r\n\r\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= (Cos<sup>2<\/sup>\u03b8 + Sin<sup>2<\/sup>\u03b8). (Cos<sup>4<\/sup>\u03b8- Cos<sup>2<\/sup>\u03b8. Sin<sup>2<\/sup>\u03b8+ Sin<sup>4<\/sup>\u03b8)<\/p>\r\n\r\n\r\n\r\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= 1. (Cos<sup>4<\/sup>\u03b8- Cos<sup>2<\/sup>\u03b8. Sin<sup>2<\/sup>\u03b8+ Sin<sup>4<\/sup>\u03b8)<\/p>\r\n\r\n\r\n\r\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= Cos<sup>4<\/sup>\u03b8- Cos<sup>2<\/sup>\u03b8. Sin<sup>2<\/sup>\u03b8+ Sin<sup>4<\/sup>\u03b8<\/p>\r\n\r\n\r\n\r\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=(Cos<sup>2<\/sup>\u03b8 + Sin<sup>2<\/sup>\u03b8)<sup>2 <\/sup>\u2013 2. Cos<sup>2<\/sup>\u03b8. Sin<sup>2<\/sup>\u03b8 &#8211; Cos<sup>2<\/sup>\u03b8. Sin<sup>2<\/sup>\u03b8<\/p>\r\n\r\n\r\n\r\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= 1-3. Cos<sup>2<\/sup>\u03b8. Sin<sup>2<\/sup>\u03b8<\/p>\r\n\r\n\r\n\r\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=R.H.S<\/p>\r\n\r\n\r\n\r\n<p><strong>\u0d8b\u0daf\u0dcf:- (6.)<\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\sqrt{\\frac{1-Cos\\;A}{1+Cos\\;A}=}Cosec\\;A-Cot\\:A<\/span><strong> \u0db6\u0dc0 \u0db4\u0dd9\u0db1\u0dca\u0dc0\u0db1\u0dca\u0db1.<\/strong><\/p>\r\n\r\n\r\n\r\n<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}L.H.S\\;&amp;=&amp;\\sqrt{\\frac{1-Cos\\;A}{1+Cos\\;A}}\\\\&amp;&amp;\\\\&amp;=&amp;\\sqrt{\\frac{\\left(1-Cos\\;A\\right)\\left(1-Cos\\;A\\right)}{\\left(1+Cos\\;A\\right)\\left(1-Cos\\;A\\right)}}\\\\&amp;&amp;\\\\&amp;=&amp;\\sqrt{\\frac{\\left(1-Cos\\;A\\right)^2}{1^2-\\left(Cos\\;A\\right)^2}}\\\\&amp;&amp;\\\\&amp;=&amp;\\frac{\\left(1-Cos\\;A\\right)}{Sin\\;A}\\\\&amp;&amp;\\\\&amp;=&amp;\\frac1{Sin\\;A}-\\frac{Cos\\;A}{Sin\\;A}\\\\&amp;&amp;\\\\&amp;=&amp;\\;Cosec\\;A\\;-Cot\\;A\\\\&amp;&amp;\\\\&amp;=&amp;R.H.S\\\\&amp;&amp;\\\\&amp;&amp;\\end{array}<\/span>\r\n\r\n\r\n\r\n<p><strong>\u0d8b\u0daf\u0dcf:- (7.) Sec <\/strong>\u03b8<strong>+ tan <\/strong>\u03b8<strong> = 2<\/strong> <strong>\u0db1\u0db8\u0dca<\/strong><strong>,<\/strong><strong> Cos <\/strong>\u03b8 <strong>\u0dc4\u0dcf tan <\/strong>\u03b8 <strong>\u0d85\u0d9c\u0dba\u0dba\u0db1\u0dca \u0dc3\u0ddc\u0dba\u0db1\u0dca\u0db1.<\/strong><\/p>\r\n\r\n\r\n\r\n<p>\u00a0 \u00a0 \u00a0Sec \u03b8+ tan \u03b8 = 2\u00a0 \u00a0 \u00a0 \u2907 \u2460<\/p>\r\n\r\n\r\n\r\n<p>\u00a02 (Sec \u03b8- tan \u03b8) = (Sec \u03b8+ tan \u03b8)( Sec \u03b8- tan \u03b8)<\/p>\r\n<p>2 (Sec \u03b8- tan \u03b8)\u00a0 =\u00a0 \u00a0Sec<sup>2<\/sup>\u03b8 &#8211; tan<sup>2<\/sup>\u03b8\u00a0<\/p>\r\n\r\n\r\n\r\n\r\n\r\n<p>\u00a0 \u00a0 \u00a0 \u00a0Sec \u03b8- tan \u03b8 = \u00bd\u00a0 \u00a0 \u2907 \u2461<\/p>\r\n<p>\u2460+\u2461\u0db1\u0dca,<\/p>\r\n\r\n\r\n\r\n\r\n\r\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a02.Sec\u03b8 = 2+ \u00bd<\/p>\r\n\r\n\r\n\r\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Sec\u03b8 = 5\/4<\/p>\r\n\r\n\r\n\r\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u2234 Cos \u03b8 = 4\/5<\/p>\r\n\r\n\r\n\r\n<p>\u00a0\u2460-\u2461\u0db1\u0dca,<\/p>\r\n\r\n\r\n\r\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a02.tan\u03b8 = 2 &#8211; \u00bd<\/p>\r\n\r\n\r\n\r\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 2tan\u03b8 = 3\/2<\/p>\r\n\r\n\r\n\r\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u2234tan\u03b8 = 3\/4<\/p>\r\n\r\n\r\n\r\n<p><strong>\u0d8b\u0daf\u0dcf:- (8.)Cos <\/strong><strong>\u03b8<\/strong><strong> =5\/13, \u0d85\u0db1\u0dd4\u0dbb\u0dd6\u0db4 Sin <\/strong><strong>\u03b8<\/strong><strong> \u0dc4\u0dcf tan <\/strong><strong>\u03b8<\/strong><strong> \u0d85\u0d9c\u0dba\u0dba\u0db1\u0dca \u0dc3\u0ddc\u0dba\u0db1\u0dca\u0db1.<\/strong><\/p>\r\n\r\n\r\n\r\n<p>Sin<sup>2<\/sup>\u03b8 + Cos<sup>2<\/sup>\u03b8 = 1<\/p>\r\n\r\n\r\n\r\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Sin<sup>2<\/sup>\u03b8 = 1 &#8211; Cos<sup>2<\/sup>\u03b8<\/p>\r\n\r\n\r\n\r\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Sin<sup>2<\/sup>\u03b8 = 1- (5\/13)<sup>2<\/sup><\/p>\r\n\r\n\r\n\r\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Sin<sup>2<\/sup>\u03b8 = 1- (25\/169)<\/p>\r\n\r\n\r\n\r\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Sin<sup>2<\/sup>\u03b8 = 144\/169<\/p>\r\n\r\n\r\n\r\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Sin \u03b8 = <span class=\"wp-katex-eq\" data-display=\"false\">\\sqrt{\\frac{144}{169}}<\/span><\/p>\r\n\r\n\r\n\r\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Sin \u03b8 = +12\/13 \u0dc4\u0ddd -12\/13<\/p>\r\n\r\n\r\n\r\n<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{l}\\sin\\;\\theta\\;=\\frac{12}{13}\\;\\text{\u0dc0\u0db1\u00a0\u0dc0\u0dd2\u0da7},\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\sin\\;\\theta\\;=-\\frac{12}{13}\\;\\text{\u0dc0\u0db1\u00a0\u0dc0\u0dd2\u0da7},\\;\\\\\\\\\\tan\\;\\theta=\\frac{\\sin\\;\\theta}{\\cos\\;\\theta}\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\tan\\;\\theta=\\frac{\\sin\\;\\theta}{\\cos\\;\\theta}\\\\\\\\\\;\\;\\;\\;\\;\\;\\;\\;\\;=\\frac{\\left({\\displaystyle\\frac{12}{13}}\\right)}{\\left({\\displaystyle\\frac5{13}}\\right)}\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;=-\\frac{\\left({\\displaystyle\\frac{12}{13}}\\right)}{\\left({\\displaystyle\\frac5{13}}\\right)}\\;\\\\\\\\\\;\\;\\;\\;\\;\\;\\;\\;\\;=\\frac{12}5\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;=-\\frac{12}5\\;\\;\\\\\\\\\\therefore\\cos\\;\\theta=\\frac5{13}\\;\\text{\u0dc0\u0db1\u00a0\u0dc0\u0dd2\u0da7,}\\\\\\\\\\;\\;\\;\\sin\\;\\theta\\;\\;=\\;\\frac{12}{13}\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\text{\u0dc4\u0ddd}\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\sin\\;\\theta\\;\\;=\\;\\frac{12}{13}\\\\\\\\\\;\\;\\;\\;\\tan\\;\\theta\\;\\;=\\;+\\frac{12}5\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\tan\\;\\theta\\;\\;=\\;-\\frac{12}5\\;\\;\\end{array}<\/span>\r\n\r\n\r\n\r\n<p><strong>\u0d8b\u0daf\u0dcf:- (<\/strong><strong>9<\/strong><strong>.)<\/strong> <strong>Sin <\/strong><strong>\u03b8<\/strong><strong> &#8211; <\/strong><strong>Cos<\/strong> <strong>\u03b8<\/strong> <strong>= a<\/strong><\/p>\r\n\r\n\r\n\r\n<p><strong>1 &#8211; Sin <\/strong><strong>\u03b8<\/strong><strong>. Cos <\/strong><strong>\u03b8 <\/strong><strong>\u00a0\u00a0\u00a0\u00a0<\/strong><strong>\u00a0= b \u00a0 \u00a0 \u0dc0\u0dda.<\/strong><\/p>\r\n\r\n\r\n\r\n<p><strong>\u0db8\u0dd9\u0db8 \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab\u0dc0\u0dbd\u0dd2\u0db1\u0dca <\/strong><strong>\u03b8<\/strong><strong> \u0d9c\u0dd9\u0db1\u0dca \u0dc3\u0dca\u0dc0\u0dcf\u0dba\u0dad\u0dca\u0dad \u0dc3\u0db8\u0dca\u0db6\u0db1\u0dca\u0db0\u0dba \u0dc3\u0ddc\u0dba\u0db1\u0dca\u0db1.<\/strong><\/p>\r\n\r\n\r\n\r\n<p>Sin \u03b8 &#8211; Cos \u03b8= a \u2907 \u2460<\/p>\r\n\r\n\r\n\r\n<p>1 &#8211; Sin \u03b8. Cos \u03b8 = b \u2907 \u2461<\/p>\r\n\r\n\r\n\r\n<p>\u2460\u0db1\u0dca,<\/p>\r\n\r\n\r\n\r\n<p>(Sin \u03b8 &#8211; Cos \u03b8)<sup>2<\/sup> = a<sup>2<\/sup><\/p>\r\n\r\n\r\n\r\n<p>Sin<sup>2<\/sup>\u03b8 + Cos<sup>2<\/sup>\u03b8 \u2013 2. Sin \u03b8. Cos \u03b8 = a<sup>2<\/sup><\/p>\r\n\r\n\r\n\r\n<p>1 &#8211; 2. Sin \u03b8. Cos \u03b8 = a<sup>2<\/sup> \u2907 \u2462<\/p>\r\n\r\n\r\n\r\n<p>\u2461x 2\u0db1\u0dca,<\/p>\r\n\r\n\r\n\r\n<p>2 &#8211; 2. Sin \u03b8. Cos \u03b8 = 2b \u2907 \u2463<\/p>\r\n\r\n\r\n\r\n<p>\u2462 &#8211; \u2463<\/p>\r\n\r\n\r\n\r\n<p>\u00a0 -1 = a<sup>2 <\/sup>\u00a0&#8211; 2b<\/p>\r\n\r\n\r\n\r\n<p>a<sup>2<\/sup> = 2b &#8211; 1<\/p>\r\n\r\n\r\n\r\n<p><strong>\u0d8b\u0daf\u0dcf:- (10.) tan <\/strong><strong>\u03b8<\/strong> <strong>+<\/strong> <strong>Cot <\/strong><strong>\u03b8<\/strong> <strong>= a<\/strong><\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0 Sec<\/strong><strong><sup>2<\/sup><\/strong><strong>\u03b8<\/strong><strong> + Cosec<\/strong><strong><sup>2<\/sup><\/strong><strong>\u03b8<\/strong> <strong>= b<\/strong><\/p>\r\n\r\n\r\n\r\n<p><strong>\u0db8\u0dd9\u0db8 \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab\u0dc0\u0dbd\u0dd2\u0db1\u0dca <\/strong><strong>\u03b8<\/strong><strong> \u0d9c\u0dd9\u0db1\u0dca \u0dc3\u0dca\u0dc0\u0dcf\u0dba\u0dad\u0dca\u0dad \u0dc3\u0db8\u0dca\u0db6\u0db1\u0dca\u0db0\u0dba \u0dc3\u0ddc\u0dba\u0db1\u0dca\u0db1.<\/strong><\/p>\r\n\r\n\r\n\r\n<p>tan \u03b8 + Cot \u03b8 = a \u2907 \u2460<\/p>\r\n\r\n\r\n\r\n<p>Sec<sup>2<\/sup>\u03b8 + Cosec<sup>2<\/sup>\u03b8 = b \u2907 \u2461<\/p>\r\n\r\n\r\n\r\n<p>\u2461\u2907<\/p>\r\n\r\n\r\n\r\n<p>1 + tan<sup>2<\/sup>\u03b8 + 1 + Cot<sup>2<\/sup>\u03b8 = b<\/p>\r\n\r\n\r\n\r\n<p>2 + tan<sup>2<\/sup>\u03b8 + Cot<sup>2<\/sup>\u03b8 = b \u2907 \u2462<\/p>\r\n\r\n\r\n\r\n<p>\u2460\u2907<\/p>\r\n\r\n\r\n\r\n<p>(tan \u03b8 + Cot \u03b8)<sup>2<\/sup> = a<sup>2<\/sup><\/p>\r\n\r\n\r\n\r\n<p>2 + tan<sup>2<\/sup>\u03b8 + Cot<sup>2<\/sup>\u03b8 = a<sup>2<\/sup> \u2907 \u2463<\/p>\r\n\r\n\r\n\r\n<p>\u2462 \u0dc4\u0dcf\u00a0 \u2463 \u0db1\u0dca,<\/p>\r\n\r\n\r\n\r\n<p>\u00a0 \u00a0 a<sup>2<\/sup>=\u00a0 b<\/p>\r\n\r\n\r\n\r\n<p>&nbsp;<\/p>\r\n\r\n<p class=\"has-background\" style=\"background-color: #272062;text-align: center\"><span style=\"color: #ffffff\"><strong><em><span style=\"font-family: 'book antiqua', palatino, serif;font-size: 18pt\">&#8220;The only laws of matter are those that our minds must fabricate and the only laws of mind are fabricated for it by matter.&#8221;<\/span><\/em><\/strong><br \/><span style=\"font-size: 10pt;font-family: tahoma, arial, helvetica, sans-serif;color: #bdbaa2\">-James Clerk Maxwell-<\/span><\/span><\/p>\r\n<p>&nbsp;<\/p>\r\n\r\n<p>Video links :<\/p>\r\n<div class=\"epyt-video-wrapper\"><iframe loading=\"lazy\"  id=\"_ytid_57114\"  width=\"696\" height=\"392\"  data-origwidth=\"696\" data-origheight=\"392\"  data-relstop=\"1\" src=\"https:\/\/www.youtube.com\/embed\/7ISBstUd9X0?enablejsapi=1&autoplay=0&cc_load_policy=0&cc_lang_pref=&iv_load_policy=1&loop=0&rel=0&fs=1&playsinline=0&autohide=2&theme=dark&color=red&controls=1&\" class=\"__youtube_prefs__  no-lazyload\" title=\"YouTube player\"  allow=\"fullscreen; accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen data-no-lazy=\"1\" data-skipgform_ajax_framebjll=\"\"><\/iframe><\/div>\r\n\r\n\r\n\r\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\">\r\n<div class=\"wp-block-embed__wrapper\"><div class=\"epyt-video-wrapper\"><iframe loading=\"lazy\"  id=\"_ytid_58312\"  width=\"696\" height=\"392\"  data-origwidth=\"696\" data-origheight=\"392\"  data-relstop=\"1\" src=\"https:\/\/www.youtube.com\/embed\/XM-FYMj0ERE?enablejsapi=1&autoplay=0&cc_load_policy=0&cc_lang_pref=&iv_load_policy=1&loop=0&rel=0&fs=1&playsinline=0&autohide=2&theme=dark&color=red&controls=1&\" class=\"__youtube_prefs__  no-lazyload\" title=\"YouTube player\"  allow=\"fullscreen; accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen data-no-lazy=\"1\" data-skipgform_ajax_framebjll=\"\"><\/iframe><\/div><\/div>\r\n<\/figure>\r\n\r\n\r\n\r\n<div class=\"wp-block-spacer\" style=\"height: 100px\" aria-hidden=\"true\">\u00a0<\/div>\r\n\r\n\r\n\r\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-block-buttons-is-layout-flex\">\r\n<div class=\"wp-block-button is-style-shadow td_btn_normal\"><a class=\"wp-block-button__link\" style=\"border-radius: 15px\" href=\"https:\/\/drive.google.com\/uc?export=download&amp;id=1uREA7gQugv5oy0w1di6xEwEAL_2sGNSR\" target=\"_blank\" rel=\"noreferrer noopener\">\u0db4\u0dcf\u0da9\u0db8\u0dda \u0dc3\u0da7\u0dc4\u0db1 Download \u0d9a\u0dbb\u0d9c\u0db1\u0dca\u0db1.<\/a><\/div>\r\n<\/div>\r\n\r\n\r\n\r\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-block-buttons-is-layout-flex\">\r\n<div class=\"wp-block-button is-style-shadow td_btn_normal\"><a class=\"wp-block-button__link\" style=\"border-radius: 15px\" href=\"https:\/\/drive.google.com\/drive\/folders\/1Pbuvhbye_zmoyMl2ILwV3MSTtfwpysXB?usp=sharing\" target=\"_blank\" rel=\"noreferrer noopener\">\u0dad\u0dc0\u0dad\u0dca \u0db4\u0dca\u200d\u0dbb\u0dc1\u0dca\u0db1 \u0db4\u0dd9\u0db1\u0dca\u0dc0\u0db1\u0dca\u0db1.<\/a><\/div>\r\n<\/div>\r\n\r\n\r\n\r\n<div class=\"wp-block-spacer\" style=\"height: 100px\" aria-hidden=\"true\">\u00a0<\/div>\r\n\r\n\r\n\r\n<p>&nbsp;<\/p>\r\n\r\n<p>&nbsp;<\/p>","protected":false},"excerpt":{"rendered":"<p>\u0d85\u0dbb\u0dca\u0dae \u0daf\u0dd0\u0d9a\u0dca\u0dc0\u0dd9\u0db1 \u0dc3\u0dd2\u0dba\u0dbd\u0dd4\u0db8 \u0d85\u0d9c\u0dba\u0db1\u0dca \u0dc3\u0daf\u0dc4\u0dcf \u0dad\u0dd8\u0db4\u0dca\u0dad \u0dc0\u0db1 \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab \u0dc3\u0dbb\u0dca\u0dc0\u0dc3\u0dcf\u0db8\u0dca\u200d\u0dba\u0db1\u0dca \u0dc0\u0dda.\u0dad\u0dca\u200d\u0dbb\u0dd2\u0d9a\u0ddd\u0dab\u0db8\u0dd2\u0dad\u0dd2\u0d9a \u0d85\u0db1\u0dd4\u0db4\u0dcf\u0dad \u0d86\u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dc0 \u0d9c\u0ddc\u0da9\u0db1\u0dd0\u0d9c\u0dd4\u0dab\u0dd4 \u0dc3\u0dbb\u0dca\u0dc0\u0dc3\u0db8\u0dca\u200d\u0dba\u0db1\u0dca \u0dc3\u0dcf\u0d9a\u0da0\u0dca\u0da1\u0dcf \u0d9a\u0dbb\u0dba\u0dd2.<\/p>\n","protected":false},"author":77,"featured_media":16558,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"tdm_status":"","tdm_grid_status":"","footnotes":""},"categories":[3644,3632,42,3630,3629],"tags":[4493,4495,4489,4490,4492,3989,4149,3993,4494,4496,3990,4491,4488],"class_list":{"0":"post-14646","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-01-04-triginometric-identities","8":"category-01-trigonometry","9":"category-advanced-level-science","10":"category-pure-mathematics","11":"category-combined-mathematics","12":"tag-cos-suthra","13":"tag-cos-","14":"tag-sarwasamya","15":"tag-sin-suthra","16":"tag-sin-","17":"tag-thrikonamithaya","18":"tag-thrikonamithiya","19":"tag-trigonometry","20":"tag-4494","21":"tag-4496","22":"tag-3990","23":"tag-4491","24":"tag-4488"},"_links":{"self":[{"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/posts\/14646"}],"collection":[{"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/users\/77"}],"replies":[{"embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/comments?post=14646"}],"version-history":[{"count":42,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/posts\/14646\/revisions"}],"predecessor-version":[{"id":37972,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/posts\/14646\/revisions\/37972"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/media\/16558"}],"wp:attachment":[{"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/media?parent=14646"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/categories?post=14646"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/tags?post=14646"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}