{"id":15632,"date":"2021-05-24T01:40:41","date_gmt":"2021-05-23T20:10:41","guid":{"rendered":"https:\/\/learnsteer.sasnaka.org\/science\/?p=15632"},"modified":"2022-01-27T01:25:09","modified_gmt":"2022-01-26T19:55:09","slug":"01-09","status":"publish","type":"post","link":"https:\/\/learnsteer.sasnaka.org\/science\/advanced-level-science\/01-09\/","title":{"rendered":"01.09.00 &#8211; \u0db4\u0dca\u200d\u0dbb\u0dad\u0dd2\u0dbd\u0ddd\u0db8 \u0dad\u0dca\u200d\u0dbb\u0dd2\u0d9a\u0ddd\u0dab\u0db8\u0dd2\u0dad\u0dd2\u0d9a \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad"},"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=1hCkvUsbXfoPjIRVoN4By5NNDP4zP2nPS\" 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 has-vivid-red-color\">\u0dc3\u0d82\u0dba\u0dd4\u0d9a\u0dca\u0dad \u0d9c\u0dab\u0dd2\u0dad\u0dba I\u00a0 (\u0dc1\u0dd4\u0daf\u0dca\u0db0 \u0d9c\u0dab\u0dd2\u0dad\u0dba)\u00a0 \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\u0dd9\u0dc4\u0dd2 \u00a0\u00a0B \u00a0\u0d9a\u0ddc\u0da7\u0dc3\u0dda(\u0dbb\u0da0\u0db1\u0dcf \u0db4\u0dca\u200d\u0dbb\u0dc1\u0dca\u0db1) 17 \u0dc0\u0dd0\u0db1\u0dd2 \u0d9c\u0dd0\u0da7\u0dc5\u0dd4\u0dc0\u0dd9\u0dc4\u0dd2 \u0db8\u0dd9\u0db8 \u0db4\u0dcf\u0da9\u0db8\u0dda \u0d85\u0da9\u0d82\u0d9c\u0dd4 \u0dc3\u0dd2\u0daf\u0dca\u0db0\u0dcf\u0db1\u0dca\u0dad \u0d85\u0da9\u0d82\u0d9c\u0dd4 \u0dc0\u0dda.<\/span><\/strong><\/li>\r\n<li>\u0d91\u0d9a\u0da7 \u0d91\u0d9a \u0dc3\u0dc4 \u0db8\u0dad\u0da7 \u0dc0\u0db1 \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba\u0d9a\u0dca \u0dc0\u0dc3\u0db8 \u0dc3\u0dc4 \u0dc3\u0dc4\u0dc0\u0dc3\u0db8 \u0dc4\u0dd4\u0dc0\u0db8\u0dcf\u0dbb\u0dd4 \u0d9a\u0dd2\u0dbb\u0dd3\u0db8\u0dd9\u0db1\u0dca \u0dbd\u0dd0\u0db6\u0dd9\u0db1 \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba \u0db4\u0dca\u200d\u0dbb\u0dad\u0dd2\u0dbd\u0ddd\u0db8 \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba \u0dc0\u0dda.<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<h2 class=\"wp-block-heading\"><strong>Sin<sup>-1<\/sup>(x ) \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba<\/strong><\/h2>\r\n\r\n\r\n\r\n<div class=\"wp-block-image\">\r\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"343\" height=\"276\" class=\"wp-image-16576\" src=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/sininverse-1.png\" alt=\"\" srcset=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/sininverse-1.png 343w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/sininverse-1-300x241.png 300w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/sininverse-1-150x121.png 150w\" sizes=\"(max-width: 343px) 100vw, 343px\" \/><\/figure>\r\n<\/div>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\mathrm{\u0dc0\u0dc3\u0db8}\\;\\lbrack-1,1\\rbrack\\;,\\;\\mathrm{\u0db4\u0dbb\u0dcf\u0dc3\u0dba}\\;\\lbrack-\\frac{\\mathrm\\pi}2,\\frac{\\mathrm\\pi}2\\rbrack<\/span><\/p>\r\n\r\n\r\n\r\n<h2 class=\"wp-block-heading\"><strong>Cos <sup>-1<\/sup>(x ) \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba<\/strong><\/h2>\r\n\r\n\r\n\r\n<div class=\"wp-block-image\">\r\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"303\" height=\"243\" class=\"wp-image-16577\" src=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/cos-inverse.png\" alt=\"\" srcset=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/cos-inverse.png 303w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/cos-inverse-300x241.png 300w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/cos-inverse-150x120.png 150w\" sizes=\"(max-width: 303px) 100vw, 303px\" \/><\/figure>\r\n<\/div>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\mathrm{\u0dc0\u0dc3\u0db8}\\;\\lbrack-1,1\\rbrack\\;,\\;\\mathrm{\u0db4\u0dbb\u0dcf\u0dc3\u0dba}\\;\\lbrack0,\\mathrm\\pi\\rbrack<\/span><\/p>\r\n\r\n\r\n\r\n<h2 class=\"wp-block-heading\"><strong>Tan <sup>-1<\/sup>(x ) \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba<\/strong><\/h2>\r\n\r\n\r\n\r\n<div class=\"wp-block-image\">\r\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"381\" height=\"292\" class=\"wp-image-16579\" src=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/taninverse.png\" alt=\"\" srcset=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/taninverse.png 381w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/taninverse-300x230.png 300w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/taninverse-150x115.png 150w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/taninverse-80x60.png 80w\" sizes=\"(max-width: 381px) 100vw, 381px\" \/><\/figure>\r\n<\/div>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\mathrm{\u0dc0\u0dc3\u0db8}\\;\\lbrack R\\rbrack\\;,\\;\\mathrm{\u0db4\u0dbb\u0dcf\u0dc3\u0dba}\\;\\lbrack-\\frac{\\mathrm\\pi}2,\\frac{\\mathrm\\pi}2\\rbrack<\/span><\/p>\r\n\r\n\r\n\r\n<p>\u0dc3\u0dbb\u0dbd \u0d9c\u0dd0\u0da7\u0dbd\u0dd4 \u0d9a\u0dd2\u0dc4\u0dd2\u0db4\u0dba\u0d9a\u0dca \u0dc3\u0dbd\u0d9a\u0dcf \u0db6\u0dbd\u0db8\u0dd4.<\/p>\r\n\r\n\r\n\r\n<ol>\r\n<li><span class=\"wp-katex-eq\" data-display=\"false\">\\;Sin^{-1}\\left(\\cos\\;\\frac\\pi3\\right)\\\\=Sin^{-1}\\left(\\frac12\\right)\\\\=\\frac\\pi6<\/span><\/li>\r\n<\/ol>\r\n\r\n\r\n\r\n\r\n\r\n<p>2. <span class=\"wp-katex-eq\" data-display=\"false\">\\;Sin^{-1}\\left(\\sin\\;\\frac{5\\pi}6\\right)\\\\=Sin^{-1}\\left[\\sin\\;\\left(\\pi-\\frac\\pi6\\right)\\right]\\\\=\\frac\\pi6<\/span><\/p>\r\n\r\n\r\n\r\n\r\n\r\n<p>3. <span class=\"wp-katex-eq\" data-display=\"false\">\\cos^{-1}\\left(\\cos\\;\\frac{4\\pi}3\\right)\\\\\\cos^{-1}\\lbrack\\cos(\\mathrm\\pi+\\frac{\\mathrm\\pi}3)\\rbrack\\\\=\\frac{2\\pi}3<\/span><\/p>\r\n<p>4.\u00a0 \u00a0<span class=\"wp-katex-eq\" data-display=\"false\">Tan^{-1}\\left(2\\sin\\frac{4\\pi}3\\right)\\\\=Tan^{-1}\\left[2\\sin\\;\\left(\\pi+\\frac\\pi3\\right)\\right]\\\\=Tan^{-1}\\left(2\\sin\\frac\\pi3\\right)\\\\=Tan^{-1}\\left(\\sqrt3\\right)\\\\=\\;\\frac\\pi3<\/span><\/p>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n<p>5. <span class=\"wp-katex-eq\" data-display=\"false\">\\sin^{-1}\\left(\\sin^{-1\\;}\\left(\\frac12\\right)\\right)\\\\=\\frac12<\/span><\/p>\r\n\r\n\r\n\r\n\r\n\r\n<p>6. <span class=\"wp-katex-eq\" data-display=\"false\">\\cos^{-1}\\left(\\cos^{-1\\;}\\left(-\\frac1{\\sqrt2}\\right)\\right)\\\\=\\frac1{\\sqrt2}<\/span><\/p>\r\n\r\n\r\n\r\n\r\n\r\n<p>\u0d85\u0dc0\u0dc3\u0dcf\u0db1\u0dba\u0da7 \u0dad\u0dca\u200d\u0dbb\u0dd2\u0d9a\u0ddd\u0dab\u0db8\u0dd2\u0dad\u0dd2\u0d9a \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba \u0d9c\u0dd0\u0db1\u0dd3\u0db8\u0dda \u0daf\u0dd3 \u0d9a\u0dca\u200d\u0dbb\u0dd2\u0dba\u0dcf\u0dc0 \u0dc3\u0dc4 \u0db4\u0dca\u200d\u0dbb\u0dad\u0dd2\u0d9a\u0dca\u200d\u0dbb\u0dd2\u0dba\u0dcf\u0dc0 \u0dbd\u0dd9\u0dc3 \u0dc3\u0dbd\u0d9a\u0dcf \u0db8\u0dd4\u0dbd\u0dca \u0d85\u0d9c\u0dba\u0db8 \u0d9c\u0dad\u0dc4\u0dd0\u0d9a\u0dd2 \u0dc0\u0dd4\u0dc0\u0daf \u0d85\u0dc0\u0dc3\u0dcf\u0db1\u0dba\u0da7 \u0db4\u0dca\u200d\u0dbb\u0dad\u0dd2\u0dbd\u0ddd\u0db8 \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba \u0d9c\u0dd0\u0db1\u0dd3\u0db8\u0dda\u0daf\u0dd3 \u0db8\u0dd4\u0dbd\u0dca \u0d85\u0d9c\u0dba \u0d85\u0db1\u0dd4\u0dbb\u0dd6\u0db4 \u0db4\u0dbb\u0dcf\u0dc3\u0dba\u0da7 \u0d85\u0dba\u0dad\u0dca \u0daf\u0dd0\u0dba\u0dd2 \u0db4\u0dbb\u0dd3\u0d9a\u0dca\u0dc2\u0dcf \u0d9a\u0dc5 \u0dba\u0dd4\u0dad\u0dd4\u0dba.<\/p>\r\n\r\n\r\n\r\n<p>\u0d8b\u0daf\u0dcf\u0dc4\u0dbb\u0dab \u0d9c\u0dd0\u0da7\u0dbd\u0dd4\u0dc0 1<\/p>\r\n\r\n\r\n\r\n<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{l}2\\cos\\;^{-1}\\left(\\frac34\\right)\\;=\\cos^{-1}\\left(\\frac18\\right)\\;\\mathrm{\u0db6\u0dc0}\\;\\mathrm{\u0db4\u0dd9\u0db1\u0dca\u0dc0\u0db1\u0dca\u0db1}\\\\\\end{array}<\/span>\r\n\r\n\r\n\r\n<p>.<\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\\mathrm A&amp;=&amp;\\cos^{-1}\\left(\\frac34\\right)\\;\\mathrm{\u0dba\u0dd0\u0dba\u0dd2}\\;\\mathrm{\u0d9c\u0db1\u0dd2\u0db8\u0dd4}.\\\\\\;\\mathrm{Cos}\\;\\mathrm A\\;&amp;=&amp;\\frac34&gt;0\\\\;0&amp;\\leq&amp;\\mathrm A\\leq\\mathrm\\pi\\;\\mathrm{\u0dc0\u0dda}.\\mathrm{\u0db1\u0db8\u0dd4\u0dad\u0dca}\\;\\;\u00be&gt;0\\;\\mathrm{\u0db1\u0dd2\u0dc3\u0dcf},\\\\\\;0&amp;&lt;&amp;\\mathrm A&lt;\\frac{\\mathrm\\pi}2\\;\\;\\;\\;\\mathrm{\u0dc0\u0dd2\u0dba}\\;\\mathrm{\u0dba\u0dd4\u0dad\u0dd4\u0dba}.\\;\\\\\\mathrm Y&amp;=&amp;2\\;\\cos^{-1}\\left(\\frac34\\right)\\\\\\mathrm Y&amp;=&amp;2\\mathrm A\\;\\\\\\mathrm{Cos}\\;\\mathrm Y\\;&amp;=&amp;\\;\\mathrm{Cos}\\;2\\mathrm A\\\\&amp;=&amp;2Cos^2A-1\\\\&amp;=&amp;2\\left(\\frac9{16}\\right)\\;\u2013\\;1\\\\\\;&amp;=&amp;\\frac18\\\\\\;0&amp;&lt;&amp;\\mathrm A&lt;\\frac{\\mathrm\\pi}2\\;\\;\\mathrm{\u0db1\u0dd2\u0dc3\u0dcf},0&lt;2\\mathrm A&lt;\\mathrm\\pi\\;\\mathrm{\u0dc0\u0dda}.\\mathrm{\u0d91\u0db1\u0db8\u0dca}\\;\\mathrm Y\\;\\mathrm{\u0d85\u0daf\u0dcf\u0dbd}\\;\\mathrm{\u0db4\u0dbb\u0dcf\u0dc3\u0dba\u0da7}\\;\\mathrm{\u0d85\u0dba\u0dad\u0dca}\\;\\mathrm{\u0dc0\u0dda}.\\;\\mathrm{\u0d92\u0db1\u0dd2\u0dc3\u0dcf},\\;\\\\\\;\\;\\mathrm Y&amp;=&amp;\\mathrm{Cos}\\;^{-1}\\left(\\frac18\\right)\\;\\mathrm{\u0dc0\u0dda}.\\\\&amp;&amp;\\end{array}<\/span><\/p>\r\n\r\n\r\n\r\n<p>\u0d8b\u0daf\u0dcf\u0dc4\u0dbb\u0dab \u0d9c\u0dd0\u0da7\u0dbd\u0dd4\u0dc0 2<\/p>\r\n\r\n\r\n\r\n<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{l}2\\tan\\;^{-1}\\left(\\frac12\\right)\\;=\\cos^{-1}\\left(\\frac35\\right)\\;\\mathrm{\u0db6\u0dc0}\\;\\mathrm{\u0db4\u0dd9\u0db1\u0dca\u0dc0\u0db1\u0dca\u0db1}\\\\\\end{array}<\/span>\r\n\r\n\r\n\r\n<p>.<\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{l}\\begin{array}{rcl}\\mathrm A&amp;=&amp;\\tan^{-1}\\left(\\frac12\\right)\\;\\mathrm{\u0dba\u0dd0\u0dba\u0dd2}\\;\\mathrm{\u0d9c\u0db1\u0dd2\u0db8\u0dd4}.\\\\\\tan\\;\\mathrm A\\;&amp;=&amp;\\frac12\\\\-\\frac{\\mathrm\\pi}2&amp;&lt;&amp;\\mathrm A&lt;\\frac{\\mathrm\\pi}2\\;\\mathrm{\u0dc0\u0dda}.\\;\\mathrm{\u0db1\u0db8\u0dd4\u0dad\u0dca}\\;\\mathrm{Tan}\\;\\mathrm A\\;\\mathrm{\u0db0\u0db1}\\;\\mathrm{\u0db1\u0dd2\u0dc3\u0dcf}\\;\\;\\begin{array}{rcl}\\;0&amp;&lt;&amp;\\mathrm A&lt;\\frac{\\mathrm\\pi}2\\;\\;\\end{array}\\mathrm{\u0dc0\u0dda}.\\;\\\\\\mathrm Y&amp;=&amp;2\\tan^{-1}\\left(\\frac12\\right)\\\\\\mathrm Y&amp;=&amp;2\\mathrm A\\;\\\\\\mathrm{Cos}\\;\\mathrm Y\\;&amp;=&amp;\\;\\mathrm{Cos}\\;2\\mathrm A\\\\&amp;=&amp;2Cos^2A-1\\\\&amp;=&amp;\\dfrac{1-\\tan^2A}{1+\\tan^2A}\\\\\\;&amp;=&amp;\\dfrac{1-{\\displaystyle\\dfrac14}}{1+{\\displaystyle\\dfrac14}}\\;\\;=\\;\\dfrac35\\\\\\;0&amp;&lt;&amp;\\mathrm A&lt;\\dfrac{\\mathrm\\pi}2\\;\\;\\mathrm{\u0db1\u0dd2\u0dc3\u0dcf},0&lt;2\\mathrm A&lt;\\mathrm\\pi\\;\\mathrm{\u0dc0\u0dda}.\\mathrm{\u0d91\u0db1\u0dd2\u0dc3\u0dcf}\\;\\mathrm Y\\;=\\cos^{-1\\;}\\left(\\dfrac35\\right)\\;\\mathrm{\u0dc0\u0dda}.\\;\\;\\\\\\;\\;\\mathrm{\u0d92\u0db1\u0db8\u0dca}\\;,2\\tan^{-1}\\left(\\dfrac12\\right)&amp;=&amp;\\mathrm{Cos}\\;^{-1}\\left(\\dfrac35\\right)\\;\\mathrm{\u0dc0\u0dda}.\\end{array}\\\\\\\\\\\\\\\\\\end{array}<\/span><\/p>\r\n\r\n\r\n\r\n<p>\u0d8b\u0daf\u0dcf\u0dc4\u0dbb\u0dab \u0d9c\u0dd0\u0da7\u0dbd\u0dd4\u0dc0 3<\/p>\r\n\r\n\r\n\r\n<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{l}Tan\\;^{-1}\\left(2\\right)\\;+Tan\\;^{-1}\\left(\\dfrac13\\right)\\;=Tan\\;^{-1}(7)\\;\\mathrm{\u0db6\u0dc0}\\;\\mathrm{\u0db4\u0dd9\u0db1\u0dca\u0dc0\u0db1\u0dca\u0db1}.\\\\\\\\\\\\\\\\\\end{array}<\/span>\r\n\r\n\r\n\r\n<p>.<\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{l}\\mathrm A=\\mathrm{Tan}\\;^{-1}(2)\\;\\\\-\\frac{\\mathrm\\pi}2&lt;\\mathrm A&lt;\\dfrac{\\mathrm\\pi}2\\;\\\\\\;\\mathrm{Tan}\\;\\mathrm A\\;=2\\;\\mathrm{\u0db0\u0db1}\\;\\mathrm{\u0db1\u0dd2\u0dc3\u0dcf},.\\;\\\\\\;0&lt;\\mathrm A&lt;\\dfrac{\\mathrm\\pi}2\\\\\\mathrm B=\\mathrm{Tan}\\;^{-1}\\left(\\dfrac13\\right)\\\\-\\dfrac{\\mathrm\\pi}2&lt;\\mathrm A&lt;\\dfrac{\\mathrm\\pi}2\\;\\\\\\;\\mathrm{TanB}\\;=\\dfrac13\\;\\mathrm{\u0db0\u0db1}\\;\\mathrm{\u0db1\u0dd2\u0dc3\u0dcf},.\\;\\\\\\;0&lt;\\mathrm B&lt;\\dfrac{\\mathrm\\pi}2\\\\\\;Tan\\;Y\\;=\\;Tan\\;(A+B)\\;\\\\=\\dfrac{Tan\\;A\\;+\\;TanB}{1\u2013\\;Tan\\;A\\;Tan\\;B\\;\\;}\\\\=\\dfrac{2+{\\displaystyle\\dfrac13}\\;\\;}{1\u20132(\\dfrac13)\\;\\;}\\\\=7\\\\\\mathrm{\u0db8\u0dd9\u0dc4\u0dd2}\\;\\mathrm A\\;\\mathrm{\u0dc4\u0dcf}\\;\\mathrm B\\;\\mathrm{\u0dc4\u0dd2}\\;\\mathrm{\u0db4\u0dbb\u0dcf\u0dc3}\\;\\mathrm{\u0db4\u0dd2\u0dc5\u0dd2\u0db6\u0db3}\\;\\mathrm{\u0dc3\u0dbd\u0d9a\u0dcf}\\;\\mathrm{\u0db6\u0dbd\u0db8\u0dd4}.\\;\\\\0&lt;A+B&lt;\\pi\\;\\;\\mathrm{\u0dc0\u0dda}.\\;\\mathrm{\u0d91\u0db1\u0db8\u0dca}\\;\\;0&lt;Y&lt;\\pi\\;\\mathrm{\u0dc0\u0dda}.\\\\\\;\\mathrm{\u0db1\u0db8\u0dd4\u0dad\u0dca}\\;Tan\\;Y\\;\\mathrm{\u0db0\u0db1}\\;\\;\\;\\;\\mathrm{\u0db1\u0dd2\u0dc3\u0dcf}\\;\\;0&lt;Y&lt;\\pi\/2\\text{ \u0dc0\u0dda. }\\\\\\text{\u0d92\u0db1\u0dd2\u0dc3\u0dcf,}Y\\;=\\;Tan\\;^{-1}(7)\\;\\mathrm{\u0dc0\u0dda}.\\\\\\;\\mathrm{\u0d91\u0db1\u0db8\u0dca},\\;\\;Tan\\;^{-1}(2)\\;+Tan\\;^{-1}\\left(\\dfrac13\\;\\right)=Tan\\;^{-1}(7)\\;\\mathrm{\u0dc0\u0dda}.\\\\\\\\\\end{array}<\/span><\/p>\r\n\r\n\r\n\r\n<p>\u0d8b\u0daf\u0dcf\u0dc4\u0dbb\u0dab \u0d9c\u0dd0\u0da7\u0dbd\u0dd4\u0dc0 4<\/p>\r\n\r\n\r\n\r\n<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{l}\\mathrm{Sin}\\;^{-1}(\u2013\\mathrm x)\\;=\\;-\\mathrm{Sin}\\;^{-1}(\\mathrm x)\\;\\mathrm{\u0db6\u0dc0}\\;\\mathrm{\u0db4\u0dd9\u0db1\u0dca\u0dc0\u0db1\u0dca\u0db1}.\\\\\\\\\\end{array}<\/span>\r\n\r\n\r\n\r\n<p>.<\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\\mathrm{Tan}\\;^{-1}(2\\mathrm x)\\;&amp;=&amp;\\mathrm A\\;\\mathrm{\u0dc4\u0dcf}\\;\\;\\mathrm{Tan}\\;^{-1}(3\\mathrm x)\\;=\\mathrm B\\;\\mathrm{\u0dbd\u0dd9\u0dc3}\\;\\mathrm{\u0d9c\u0db1\u0dd2\u0db8\u0dd4}.\\\\-\\frac{\\mathrm\\pi}2&amp;&lt;&amp;\\mathrm A&lt;\\frac{\\mathrm\\pi}2\\;\\\\Tan\\;\\mathrm A\\;&amp;=&amp;\\;2\\mathrm x-\\\\\\frac{\\mathrm\\pi}2&amp;&lt;&amp;\\mathrm B&lt;\\frac{\\mathrm\\pi}2\\\\Tan\\;\\mathrm B\\;&amp;=&amp;\\;3\\mathrm x\\\\\\mathrm A+\\mathrm B&amp;=&amp;\\;\\frac{\\mathrm\\pi}4\\\\Tan(\\mathrm A+\\mathrm B)&amp;=&amp;\\mathrm{Tan}\\;\\frac{\\mathrm\\pi}4\\;\\\\\\mathrm{Tan}\\;\\mathrm A\\;+\\mathrm{Tan}\\;\\mathrm B1\u2013\\;\\mathrm{Tan}\\;\\mathrm A\\;\\mathrm{Tan}\\;\\mathrm B\\;&amp;=&amp;\\;1\\\\;2\\mathrm x+3\\mathrm x1\u20132\\mathrm x.3\\mathrm x&amp;=&amp;1\\\\5\\mathrm x&amp;=&amp;1\u20136\\mathrm x^2\\;\\\\6\\mathrm x^2+5\\mathrm x\u20131&amp;=&amp;0\\\\(6\\mathrm x\u20131)(\\mathrm x+1)&amp;=&amp;0\\\\\\mathrm X&amp;=&amp;\\frac16\\;\\mathrm{\u0dc4\u0ddd}\\;\\mathrm x=(\u20131)\\end{array}<\/span><\/p>\r\n\r\n\r\n\r\n<p>\u0d8b\u0daf\u0dcf\u0dc4\u0dbb\u0dab \u0d9c\u0dd0\u0da7\u0dbd\u0dd4\u0dc0 5<\/p>\r\n\r\n\r\n\r\n<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\\mathrm{Sin}\\;^{-1}(\\mathrm x)\\;+\\;\\mathrm{Cos}\\;^{-1}(\\mathrm x)\\;&amp;=&amp;\\;\\frac{\\mathrm\\pi}2\\;\\mathrm{\u0db6\u0dc0}\\;\\mathrm{\u0db4\u0dd9\u0db1\u0dca\u0dc0\u0db1\u0dca\u0db1}.\\\\&amp;&amp;\\\\&amp;&amp;\\end{array}<\/span>\r\n\r\n\r\n\r\n<p>.<\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}Sin^{-1}(x)\\;&amp;=&amp;\\;A\\;\\mathrm{\u0dba\u0dd0\u0dba\u0dd2}\\;\\mathrm{\u0d9c\u0db1\u0dd2\u0db8\u0dd4}.\\\\-\\frac\\pi2&amp;\\leq&amp;A\\leq\\frac\\pi2\\;\\\\\\frac\\pi2&amp;\\geq&amp;(\u2013A)\\geq\u2013\\frac\\pi2\\\\&amp;&amp;\\mathrm{\u0daf\u0dd9\u0db4\u0dc3\u0da7}\\;\\mathrm \u0db8\\;\\frac{\\mathrm\\pi}2\\;\\mathrm{\u0d9a\u0dca}\\;\\mathrm{\u0d91\u0d9a\u0dad\u0dd4}\\;\\mathrm{\u0d9a\u0dbb\u0db8\u0dd4}.\\\\\\pi&amp;\\geq&amp;(\\frac{\\mathrm\\pi}2\u2013A)\\geq0\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\\\Sin\\;A\\;&amp;=&amp;\\;X\\;\\\\Cos\\;\\left(\\frac{\\mathrm\\pi}2\u2013A\\right)\\;\\;&amp;=&amp;\\;X\\\\\\;Cos^{\\;-1}\\left[\\cos\\left(\\frac{\\mathrm\\pi}2\u2013A\\right)\\right]&amp;=&amp;Cos^{\\;-1}(x)\\\\\\frac{\\mathrm\\pi}2\u2013A\\;&amp;=&amp;\\;Cos^{-1}(x)\\;\\\\\\frac{\\mathrm\\pi}2&amp;=&amp;\\;A\\;+\\;Cos^{-1}(x)\\;\\\\&amp;&amp;\\text{\u0d91\u0db8\u0db1\u0dd2\u0dc3\u0dcf,}\\;\\\\Sin\\;^{-1}(x)\\;+\\;Cos\\;^{-1}(x)\\;&amp;=&amp;\\;\\frac{\\mathrm\\pi}2\\;\\mathrm{\u0dc0\u0dda}.\\end{array}<\/span><\/p>\r\n\r\n\r\n\r\n<div class=\"wp-block-cover has-cyan-bluish-gray-background-color has-background-dim\">\r\n<div class=\"wp-block-cover__inner-container is-layout-flow wp-block-cover-is-layout-flow\">\r\n<div class=\"wp-block-image\">\r\n<figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-31142\" src=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/09\/Img_1.jpg-1024x721.jpeg\" alt=\"\" width=\"300\" height=\"200\" \/><\/figure>\r\n<\/div>\r\n\r\n\r\n\r\n<p class=\"has-text-color\" style=\"color: #072d4c;font-size: 20px\"><strong>\u0db8\u0dd9\u0db8 \u0dc3\u0dd8\u0da2\u0dd4\u0d9a\u0ddd\u0dab\u0dcf\u0dc3\u0dca\u200d\u0dbb\u0dba \u0dad\u0dd4\u0dc5 \u0d91\u0d9a \u0dc3\u0db8\u0dcf\u0db1 \u0dc3\u0dd4\u0daf\u0dd4 \u0db4\u0dd0\u0dc4\u0dd0 \u0dc3\u0db8\u0da0\u0dad\u0dd4\u0dbb\u0dc3\u0dca\u200d\u0dbb 7\u0d9a\u0dca \u0dad\u0dd2\u0db6\u0dd9\u0db1\u0dc0\u0dcf. \u0d94\u0db6\u0da7 \u0dbd\u0dd0\u0db6\u0dd9\u0db1 \u0d85\u0db7\u0dd2\u0dba\u0ddd\u0d9c\u0dba \u0dc0\u0db1\u0dca\u0db1\u0dda \u0d91\u0d9a\u0dca \u0dc3\u0dd4\u0daf\u0dd4 \u0db4\u0dd0\u0dc4\u0dd0 \u0dc3\u0db8\u0da0\u0dad\u0dd4\u0dbb\u0dc3\u0dca\u200d\u0dbb\u0dba\u0d9a \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba \u0dc3\u0dd9\u0dc0\u0dd3\u0db8\u0dba\u0dd2.<\/strong><\/p>\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-background\" style=\"border-radius: 10px;background: linear-gradient(135deg,#0693e3 0%,#072d4c 0%)\" href=\"https:\/\/learnsteer.sasnaka.org\/science\/?p=31140\" 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\r\n\r\n\r\n<p>&nbsp;<\/p>\r\n<\/div>\r\n<\/div>\r\n\r\n\r\n\r\n<h2 class=\"wp-block-heading\"><strong>\u0db4\u0dca\u200d\u0dbb\u0dad\u0dd2\u0dbd\u0ddd\u0db8 \u0dad\u0dca\u200d\u0dbb\u0dd2\u0d9a\u0ddd\u0dab\u0db8\u0dd2\u0dad\u0dd2\u0d9a \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab \u0dc0\u0dd2\u0dc3\u0db3\u0dd3\u0db8.<\/strong><\/h2>\r\n\r\n\r\n\r\n<p>\u0d8b\u0daf\u0dcf\u0dc4\u0dbb\u0dab \u0d9c\u0dd0\u0da7\u0dbd\u0dd4\u0dc0 6<\/p>\r\n\r\n\r\n\r\n<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}Tan^{\\;-1}(2x)\\;+\\;Tan\\;^{-1}(3x)\\;&amp;=&amp;\\;\\frac{\\pi\\;}4\\text{\u0dc0\u0dd2\u0dc3\u0db3\u0db1\u0dca\u0db1.}\\\\&amp;&amp;\\end{array}<\/span>\r\n\r\n\r\n\r\n<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\\mathrm{Tan}\\;^{-1}(2\\mathrm x)\\;&amp;=&amp;\\mathrm A\\;\\mathrm{\u0dc4\u0dcf}\\;\\;\\mathrm{Tan}\\;^{-1}(3\\mathrm x)\\;=\\mathrm B\\;\\mathrm{\u0dbd\u0dd9\u0dc3}\\;\\mathrm{\u0d9c\u0db1\u0dd2\u0db8\u0dd4}.\\\\-\\frac{\\mathrm\\pi}2&amp;&lt;&amp;\\mathrm A&lt;\\frac{\\mathrm\\pi}2\\;\\\\\\mathrm{Tan}\\;\\mathrm A\\;&amp;=&amp;\\;2\\mathrm x\\\\-\\frac{\\mathrm\\pi}2&amp;&lt;&amp;\\mathrm B&lt;\\frac{\\mathrm\\pi}2\\\\\\mathrm{Tan}\\;\\mathrm B\\;&amp;=&amp;\\;3\\mathrm x\\\\\\;\\;\\mathrm A+\\mathrm B&amp;=&amp;\\;\\frac{\\mathrm\\pi}4\\\\\\mathrm{Tan}(\\mathrm A+\\mathrm B)&amp;=&amp;\\mathrm{Tan}\\;\\frac{\\mathrm\\pi}4\\;\\\\\\frac{\\mathrm{Tan}\\;\\mathrm A\\;+\\mathrm{Tan}\\;\\mathrm B}{1\u2013\\;\\mathrm{Tan}\\;\\mathrm A\\;\\mathrm{Tan}\\;\\mathrm B}\\;&amp;=&amp;\\;1\\\\\\frac{\\;2\\mathrm x+3\\mathrm x}{1\u20132\\mathrm x.3\\mathrm x}&amp;=&amp;1\\\\\\;5\\mathrm x&amp;=&amp;1\u20136\\mathrm x^2\\;\\\\6\\mathrm x^2+5\\mathrm x\u20131&amp;=&amp;0\\\\\\;(6\\mathrm x\u20131)(\\mathrm x+1)&amp;=&amp;0\\\\\\;\\mathrm X&amp;=&amp;\\frac16\\;\\mathrm{\u0dc4\u0ddd}\\;\\mathrm x=(\u20131)\\end{array}<\/span>\r\n\r\n\r\n\r\n<p>\u0daf\u0dd0\u0db1\u0dca \u0db8\u0dd9\u0db8 \u0dbd\u0dd0\u0db6\u0dd4\u0dab\u0dd4 \u0db4\u0dd2\u0dc5\u0dd2\u0dad\u0dd4\u0dbb\u0dd4 \u0db4\u0dc5\u0db8\u0dd4 \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab\u0dba \u0dad\u0dd8\u0db4\u0dca\u0dad \u0d9a\u0dbb\u0db1\u0dca\u0db1\u0dda \u0daf\u0dd0\u0dba\u0dd2 \u0db4\u0dbb\u0dd3\u0d9a\u0dca\u0dc2\u0dcf \u0d9a\u0dc5 \u0dba\u0dd4\u0dad\u0dd4\u0dba\u0dd2.<\/p>\r\n\r\n\r\n\r\n<p>\u0d91\u0dc3\u0dda \u0db4\u0dbb\u0dd3\u0d9a\u0dca\u0dc2\u0dcf \u0d9a\u0dd2\u0dbb\u0dd3\u0db8\u0dd9\u0db1\u0dca \u0db4\u0dc3\u0dd4 x = (\u20131) \u0db4\u0dd2\u0dc5\u0dd2\u0d9c\u0dad \u0db1\u0ddc\u0dc4\u0dd0\u0d9a\u0dd2 \u0db6\u0dc0 \u0db4\u0dd9\u0db1\u0dda.\u0d92\u0db1\u0dd2\u0dc3\u0dcf,\u0db8\u0dd9\u0dc4\u0dd2 \u0db4\u0dd2\u0dc5\u0dd2\u0dad\u0dd4\u0dbb ,x= 1\/6 \u0dc0\u0dda.<\/p>\r\n\r\n\r\n\r\n<p>\u0d8b\u0daf\u0dcf\u0dc4\u0dbb\u0dab \u0d9c\u0dd0\u0da7\u0dbd\u0dd4\u0dc0 7<\/p>\r\n\r\n\r\n\r\n<span class=\"wp-katex-eq\" data-display=\"false\">Tan\\;^{-1}\\sqrt{x+2}\\;\\;+\\;Tan\\;^{-1}\\sqrt{\\frac1{2x+1}\\;}\\;=\\;\\frac\\pi2\\;\\;\\;\\;\\mathrm{\u0dc0\u0dd2\u0dc3\u0db3\u0db1\u0dca\u0db1}<\/span>\r\n\r\n\r\n\r\n<p>.<\/p>\r\n\r\n\r\n\r\n<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\\mathrm{Tan}\\;^{-1}\\sqrt{\\mathrm x+2\\;}&amp;=&amp;\\;\\;\\mathrm A\\;\\;\\mathrm \u0daf,\\;\\\\-\\frac{\\mathrm\\pi}2&amp;&lt;&amp;\\mathrm A&lt;\\frac{\\mathrm\\pi}2\\;\\\\\\;\\mathrm{Tan}\\;\\mathrm A\\;&amp;=&amp;\\;\\sqrt{\\mathrm x+2\\;}\\\\\\mathrm{Tan}\\;^{-1}\\sqrt{\\frac1{2\\mathrm x+1}}\\;\\;&amp;=&amp;\\;\\mathrm B\\;\\;\\;\\mathrm \u0daf\\;\\mathrm{\u0dbd\u0dd9\u0dc3}\\;\\mathrm{\u0d9c\u0db1\u0dd2\u0db8\u0dd4}.\\;\\\\-\\frac{\\mathrm\\pi}2&amp;&lt;&amp;\\mathrm A&lt;\\frac{\\mathrm\\pi}2\\;\\;\\\\\\mathrm{Tan}\\;\\mathrm B\\;&amp;=&amp;\\;\\sqrt{\\frac1{2\\mathrm x+1}}\\;\\;\\;\\;\\;\\;\\;\u2907\\;\u2460\\\\\\;\\mathrm A\\;+\\;\\mathrm B\\;&amp;=&amp;\\;\\frac{\\mathrm\\pi}2\\\\\\mathrm A\\;&amp;=&amp;\\;\\frac{\\mathrm\\pi}2\\;\u2013\\;\\mathrm B\\;\\\\\\mathrm{Tan}\\;\\mathrm A\\;&amp;=&amp;\\;\\mathrm{Tan}(\\frac{\\mathrm\\pi}2\\;\u2013\\;\\mathrm B)\\;\\\\\\;\\mathrm{Tan}\\;\\mathrm A\\;&amp;=&amp;\\;\\mathrm{CotB}\\;\\\\\\;\\therefore\\;\\;\\mathrm{CotB}\\;&amp;=&amp;\\;\\sqrt{\\mathrm x+2}\\;\\;\\;\u2907\\;\u2461\\\\&amp;&amp;\\;\u2460\\;\\;\\mathrm{\u0dc4\u0dcf}\\;\u2461\\;\\mathrm{\u0db1\u0dca},\\\\\\;\\;\\frac1{\\sqrt{2\\mathrm x+1}}&amp;=&amp;\\;\\frac{\\;1}{\\mathrm x+2}\\;\\;\\;\\;\\\\2\\mathrm x\\;+\\;1\\;\\;&amp;=&amp;\\;\\mathrm x\\;+\\;2\\;\\\\\\mathrm x\\;&amp;=&amp;\\;1\\;\\\\&amp;&amp;\\mathrm{\u0db8\u0dd9\u0db8}\\;\\mathrm{\u0dc0\u0dd2\u0dc3\u0daf\u0dd4\u0db8}\\;\\mathrm{\u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab\u0dba}\\;\\mathrm{\u0dad\u0dd8\u0db4\u0dca\u0dad}\\;\\mathrm{\u0d9a\u0dbb\u0dba\u0dd2}.\\end{array}<\/span>\r\n\r\n\r\n\r\n<p>\u0db4\u0dc3\u0dd4\u0d9c\u0dd2\u0dba \u0dc0\u0dd2\u0db7\u0dcf\u0d9c \u0d9c\u0dd0\u0da7\u0dbd\u0dd4\u0dc0\u0d9a\u0dca \u0dc3\u0dbd\u0d9a\u0dcf \u0db6\u0dbd\u0db8\u0dd4<\/p>\r\n\r\n\r\n\r\n<p>2018 AL \/ I\u00a0 \u0d9a\u0ddc\u0da7\u0dc3 \/ (17) C<\/p>\r\n\r\n\r\n\r\n<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}2Tan\\;^{-1}\\left(\\frac13\\right)\\;+\\;Tan\\;^{-1}\\frac43&amp;=&amp;\\;\\frac\\pi2\\;\u0db6\\mathrm \u0dc0\\;\\mathrm{\u0db4\u0dd9\u0db1\u0dca\u0dc0\u0db1\u0dca\u0db1}\\end{array}<\/span>\r\n\r\n\r\n\r\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"789\" height=\"415\" class=\"wp-image-15779\" src=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/image-226.png\" alt=\"\" srcset=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/image-226.png 789w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/image-226-300x158.png 300w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/image-226-768x404.png 768w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/image-226-150x79.png 150w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/image-226-696x366.png 696w\" sizes=\"(max-width: 789px) 100vw, 789px\" \/><\/figure>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center has-white-color has-text-color has-background\" style=\"background-color: #272062\"><span style=\"color: #ffffff\"><em><strong><span style=\"font-family: 'book antiqua', palatino, serif;font-size: 18pt\">\u00a0\u201cA mathematical theory is not to be considered complete until you have made it so clear that you can explain it to the first man whom you meet on the street.\u201d<\/span><\/strong><\/em><\/span><br \/><span style=\"font-family: tahoma, arial, helvetica, sans-serif;font-size: 10pt;color: #808080\">-David Hilbert &#8211;<\/span><\/p>\r\n\r\n\r\n\r\n<div class=\"wp-block-spacer\" style=\"height: 100px\" aria-hidden=\"true\"><div class=\"epyt-video-wrapper\"><iframe loading=\"lazy\"  id=\"_ytid_22979\"  width=\"696\" height=\"392\"  data-origwidth=\"696\" data-origheight=\"392\"  data-relstop=\"1\" src=\"https:\/\/www.youtube.com\/embed\/x-w_S9w3Hpo?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<div aria-hidden=\"true\">\u00a0<\/div>\r\n<div aria-hidden=\"true\">\u00a0<\/div>\r\n<div aria-hidden=\"true\">\u00a0<\/div>\r\n<div aria-hidden=\"true\">\u00a0<\/div>\r\n<div aria-hidden=\"true\">\u00a0<\/div>\r\n<div aria-hidden=\"true\">\u00a0<\/div>\r\n<div aria-hidden=\"true\">\u00a0<\/div>\r\n<div aria-hidden=\"true\">\u00a0<\/div>\r\n<div aria-hidden=\"true\">\u00a0<\/div>\r\n<div aria-hidden=\"true\">\u00a0<\/div>\r\n<div aria-hidden=\"true\">\u00a0<\/div>\r\n<div aria-hidden=\"true\">\u00a0<\/div>\r\n<div aria-hidden=\"true\">\u00a0<\/div>\r\n<div aria-hidden=\"true\">\u00a0<\/div>\r\n<div aria-hidden=\"true\">\u00a0<\/div>\r\n<div aria-hidden=\"true\">\u00a0<\/div>\r\n<div aria-hidden=\"true\">\u00a0<\/div>\r\n<div aria-hidden=\"true\">\u00a0<\/div>\r\n<div aria-hidden=\"true\">\u00a0<\/div>\r\n<div aria-hidden=\"true\"><div class=\"epyt-video-wrapper\"><iframe loading=\"lazy\"  id=\"_ytid_77044\"  width=\"696\" height=\"392\"  data-origwidth=\"696\" data-origheight=\"392\"  data-relstop=\"1\" src=\"https:\/\/www.youtube.com\/embed\/ijMchHuYCSQ?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\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=1hCkvUsbXfoPjIRVoN4By5NNDP4zP2nPS\" 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","protected":false},"excerpt":{"rendered":"<p>\u0dc0\u0dc3\u0db8 \u0dc4\u0dcf \u0db4\u0dbb\u0dcf\u0dc3\u0dba \u0db8\u0dcf\u0dbb\u0dd4 \u0d9a\u0dd2\u0dbb\u0dd3\u0db8\u0dd9\u0db1\u0dca \u0db1\u0dd2\u0dbb\u0dca\u0db8\u0dcf\u0dab\u0dba \u0dc0\u0db1 \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba \u0daf\u0dd3 \u0d87\u0dad\u0dd2 \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba\u0dda \u0db4\u0dca\u200d\u0dbb\u0dad\u0dd2\u0dbd\u0ddd\u0db8 \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba \u0db1\u0db8\u0dca \u0dc0\u0dda.\u0d91\u0d9a\u0da7 \u0d91\u0d9a \u0dc4\u0dcf \u0db8\u0dad\u0da7 \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad \u0dc3\u0daf\u0dc4\u0dcf \u0db4\u0db8\u0dab\u0d9a\u0dca \u0d85\u0dbb\u0dca\u0dae \u0daf\u0dd0\u0d9a\u0dca\u0dc0\u0dd9\u0db1 \u0dc4\u0dd9\u0dba\u0dd2\u0db1\u0dca \u0db4\u0dca\u200d\u0dbb\u0dad\u0dd2\u0dbd\u0ddd\u0db8 \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad \u0db1\u0dd2\u0dbb\u0dca\u0db8\u0dcf\u0dab\u0dba\u0dda\u0daf\u0dd3 \u0dc3\u0dd4\u0daf\u0dd4\u0dc3\u0dd4 \u0db4\u0dbb\u0dd2\u0daf\u0dd2 \u0dc0\u0dc3\u0db8\u0dba \u0dad\u0ddd\u0dbb\u0dcf\u0d9c\u0dad \u0dba\u0dd4\u0dad\u0dd4\u0dba.\u0db4\u0dca\u200d\u0dbb\u0db0\u0dcf\u0db1 \u0dad\u0dca\u200d\u0dbb\u0dd2\u0d9a\u0ddd\u0dab\u0db8\u0dd2\u0dad\u0dd2\u0d9a \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad \u0dc3\u0daf\u0dc4\u0dcf \u0db4\u0dca\u200d\u0dbb\u0dad\u0dd2\u0dbd\u0ddd\u0db8 \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad \u0db4\u0dd2\u0dc5\u0dd2\u0db6\u0daf \u0db8\u0dd9\u0dc4\u0dd2\u0daf\u0dd3 \u0d85\u0db0\u0dca\u200d\u0dba\u0db1\u0dba \u0d9a\u0dbb\u0dba\u0dd2.<\/p>\n","protected":false},"author":21,"featured_media":16558,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"tdm_status":"","tdm_grid_status":"","footnotes":""},"categories":[3649,3632,42,3630,3629],"tags":[4543,4544,4540,4538,4542,4541,4500,4539],"class_list":{"0":"post-15632","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-01-09-inverse-trigonometric-functions","8":"category-01-trigonometry","9":"category-advanced-level-science","10":"category-pure-mathematics","11":"category-combined-mathematics","12":"tag-cosx","13":"tag-inverse-function","14":"tag-prathiloma-shritha","15":"tag-sin-1x-","16":"tag-sinx","17":"tag-trikonamithika-prathiloma-shritha","18":"tag-trikonamithiya","19":"tag-4539"},"_links":{"self":[{"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/posts\/15632"}],"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\/21"}],"replies":[{"embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/comments?post=15632"}],"version-history":[{"count":54,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/posts\/15632\/revisions"}],"predecessor-version":[{"id":35303,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/posts\/15632\/revisions\/35303"}],"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=15632"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/categories?post=15632"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/tags?post=15632"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}