{"id":37164,"date":"2022-11-29T19:03:33","date_gmt":"2022-11-29T13:33:33","guid":{"rendered":"https:\/\/yanamtakshashila.com\/?p=37164"},"modified":"2022-11-30T11:10:44","modified_gmt":"2022-11-30T05:40:44","slug":"unit-iii-trigonometry-formulae","status":"publish","type":"post","link":"https:\/\/yanamtakshashila.com\/?p=37164","title":{"rendered":"UNIT \u2013 III TRIGONOMETRY (Formulae)"},"content":{"rendered":"\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\LARGE{\\color {purple} {TRIGONOMETRIC\\ IDENTITIES}}\\]<script src=\"https:\/\/yanamtakshashila.com\/wp-includes\/js\/dist\/hooks.min.js?ver=dd5603f07f9220ed27f1\" id=\"wp-hooks-js\"><\/script>\n<script src=\"https:\/\/yanamtakshashila.com\/wp-includes\/js\/dist\/i18n.min.js?ver=c26c3dc7bed366793375\" id=\"wp-i18n-js\"><\/script>\n<script id=\"wp-i18n-js-after\">\nwp.i18n.setLocaleData( { 'text direction\\u0004ltr': [ 'ltr' ] } );\n\/\/# sourceURL=wp-i18n-js-after\n<\/script>\n<script  async src=\"https:\/\/cdnjs.cloudflare.com\/ajax\/libs\/mathjax\/2.7.7\/MathJax.js?config=TeX-MML-AM_CHTML\" id=\"mathjax-js\"><\/script>\n<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color {royalblue} {Fundamental\\ Trigonometrical\\ identities}:\\ \\hspace{20cm}\\] <\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[sin^2\u03b8\\ +\\  cos^2\u03b8\\ =\\  1\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[1\\ +\\  tan^2\u03b8\\ =\\  sec^2\u03b8\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[1\\ +\\  cot^2\u03b8\\ =\\  cosec^2\u03b8\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color {royalblue} {Trigonometrical\\  ratios\\  of\\  known\\  angles}:\\ \\hspace{20cm}\\] <\/div>\n\n\n\n<figure class=\"wp-block-image alignfull size-full\"><img data-recalc-dims=\"1\" fetchpriority=\"high\" decoding=\"async\" width=\"768\" height=\"432\" data-attachment-id=\"37186\" data-permalink=\"https:\/\/yanamtakshashila.com\/?attachment_id=37186\" data-orig-file=\"https:\/\/i0.wp.com\/yanamtakshashila.com\/wp-content\/uploads\/2022\/11\/image-4.png?fit=768%2C432&amp;ssl=1\" data-orig-size=\"768,432\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"image-4\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/yanamtakshashila.com\/wp-content\/uploads\/2022\/11\/image-4.png?fit=768%2C432&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/yanamtakshashila.com\/wp-content\/uploads\/2022\/11\/image-4.png?resize=768%2C432&#038;ssl=1\" alt=\"\" class=\"wp-image-37186\" srcset=\"https:\/\/i0.wp.com\/yanamtakshashila.com\/wp-content\/uploads\/2022\/11\/image-4.png?w=768&amp;ssl=1 768w, https:\/\/i0.wp.com\/yanamtakshashila.com\/wp-content\/uploads\/2022\/11\/image-4.png?resize=649%2C365&amp;ssl=1 649w, https:\/\/i0.wp.com\/yanamtakshashila.com\/wp-content\/uploads\/2022\/11\/image-4.png?resize=500%2C280&amp;ssl=1 500w, https:\/\/i0.wp.com\/yanamtakshashila.com\/wp-content\/uploads\/2022\/11\/image-4.png?resize=600%2C338&amp;ssl=1 600w\" sizes=\"(max-width: 768px) 100vw, 768px\" \/><\/figure>\n\n\n\n<script async=\"\" src=\"https:\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js?client=ca-pub-9453835310745500\" crossorigin=\"anonymous\"><\/script>\n<ins class=\"adsbygoogle\" style=\"display:inline-block;width:300px;height:250px\" data-ad-client=\"ca-pub-9453835310745500\" data-ad-slot=\"5990643685\"><\/ins>\n<script>\n     (adsbygoogle = window.adsbygoogle || []).push({});\n<\/script>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[Sin ( A + B )\\  =\\  Sin A\\  Cos B\\ +\\  Cos A\\  Sin B\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[Sin ( A &#8211; B )\\  =\\  Sin A\\ Cos B\\ -\\  Cos A\\ Sin B\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[Cos( A + B )\\  =\\  Cos A\\ Cos B\\ -\\  Sin A Sin B\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[Cos( A &#8211; B )\\  =\\  Cos A\\ Cos B\\ +\\  Sin A Sin B\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[Tan(A + B)\\ =\\ \\frac{Tan A\\ +\\ Tan B}{1\\ -\\ Tan A\\ Tan B}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[Tan(A &#8211; B)\\ =\\ \\frac{Tan A\\ -\\ Tan B}{1\\ +\\ Tan A\\ Tan B}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color {brown} {Note}:\\ Sin\\ ( &#8211; \u03b8 )\\  =\\  -\\ sin\\ \u03b8\\ \\hspace{2cm}\\ cos\\ ( &#8211;  \u03b8 )\\  =\\  cos\\ \u03b8\\]<\/div>\n\n\n\n<script async=\"\" src=\"https:\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js?client=ca-pub-9453835310745500\" crossorigin=\"anonymous\"><\/script>\n<ins class=\"adsbygoogle\" style=\"display:block; text-align:center;\" data-ad-layout=\"in-article\" data-ad-format=\"fluid\" data-ad-client=\"ca-pub-9453835310745500\" data-ad-slot=\"6565358754\"><\/ins>\n<script>\n     (adsbygoogle = window.adsbygoogle || []).push({});\n<\/script>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color {royalblue} {Multiple\\ Angles\\ of\\ 2A}:\\ \\hspace{20cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[1\\ (i)\\ Sin\\ 2A\\  =\\  2\\ Sin\\ A\\  Cos\\ A\\ \\hspace{5cm}\\ (ii)\\ Sin\\ 2A\\  =\\ \\frac{2\\ Tan\\ A}{1\\ +\\ Tan^2\\ A}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[2\\ (i)\\ Cos\\ 2A\\  =\\ Cos^2A\\ -\\  Sin^2A\\ \\hspace{5cm}\\ (ii)\\ Cos\\ 2A\\  =\\ \\frac{1\\ -\\ Tan^2A}{1\\ +\\ Tan^2\\ A}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[3.\\ Tan\\ 2A\\  =\\ \\frac{2\\ Tan\\ A}{1\\ -\\ Tan^2\\ A}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[4.\\ Sin^2A\\  =\\ \\frac{1\\ -\\ Cos\\ 2A}{2}\\ \\hspace{5cm}\\ Note:\\ 1\\ -\\ 2\\ Sin^2A\\ =\\ Cos\\ 2A\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[5.\\ Cos^2A\\  =\\ \\frac{1\\ +\\ Cos\\ 2A}{2}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[6.\\ Tan^2A\\  =\\ \\frac{1\\ -\\ Cos\\ 2A}{1\\ +\\ Cos\\ 2A}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color {royalblue} {Multiple\\ Angles\\ of\\ 3A}:\\ \\hspace{20cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[1.\\ Sin\\ 3\\ \\theta\\  =\\ 3\\ Sin\\ \\theta\\  -\\ 4\\ Sin^3\\ \\theta\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[2.\\ Cos\\ 3\\ \\theta\\  =\\ 4\\ Cos^3\\ \\theta\\  -\\ 3\\ Cos\\ \\theta\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[3.\\ tan\\ 3\\ \\theta\\  =\\ \\frac{3\\ tan\\ \\theta\\ -\\ tan^3\\ \\theta}{1\\ -\\ 3\\ tan^2\\ \\theta}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<script async=\"\" src=\"https:\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js?client=ca-pub-9453835310745500\" crossorigin=\"anonymous\"><\/script>\n<!-- Leader board 1 -->\n<ins class=\"adsbygoogle\" style=\"display:inline-block;width:728px;height:90px\" data-ad-client=\"ca-pub-9453835310745500\" data-ad-slot=\"8769628924\"><\/ins>\n<script>\n     (adsbygoogle = window.adsbygoogle || []).push({});\n<\/script>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\LARGE{\\color {purple} {INVERSE\\ TRIGONOMETRIC\\ FUNCTIONS}}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color {royalblue} {Sum\\ and\\ Product\\ Identities}:\\ \\hspace{20cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[1.\\ Sin\\ A\\ +\\ Sin\\ B =\\ 2\\ Sin\\ (\\frac{A\\ +\\ B}{2})\\ Cos\\ (\\frac{A\\ -\\ B}{2})\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[2.\\ Sin\\ A\\ -\\ Sin\\ B =\\ 2\\ Cos\\ (\\frac{A\\ +\\ B}{2})\\ Sin\\ (\\frac{A\\ -\\ B}{2})\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[3.\\ Cos\\ A\\ +\\ Cos\\ B =\\ 2\\ Cos\\ (\\frac{A\\ +\\ B}{2})\\ Cos\\ (\\frac{A\\ -\\ B}{2})\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[4.\\ Cos\\ A\\ -\\ Cos\\ B =\\ -\\ 2\\ Sin\\ (\\frac{A\\ +\\ B}{2})\\ Sin\\ (\\frac{A\\ -\\ B}{2})\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[5.\\ Sin\\ A\\ Cos\\ B\\ =\\ \\frac{1}{2}[Sin\\ (A\\ +\\ B)\\ +\\ Sin\\ (A\\ -\\ B)]\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[7.\\ Cos\\ A\\ Cos\\ B\\ =\\ \\frac{1}{2}[Cos\\ (A\\ +\\ B)\\ +\\ Cos\\ (A\\ -\\ B)]\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[8.\\ Sin\\ A\\ Sin\\ B\\ =\\ \\frac{-\\ 1}{2}[Cos\\ (A\\ +\\ B)\\ -\\ Cos\\ (A\\ -\\ B)]\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[9.\\ Sin\\ (A\\ +\\ B)Sin\\ (A\\ -\\ B)\\ =\\ Sin^2\\ A\\ -\\  Sin^2\\ B\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[10.\\ Cos\\ (A\\ +\\ B)Cos\\ (A\\ -\\ B)\\ =\\ Cos^2\\ A\\ -\\  Sin^2\\ B\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<script async src=\"https:\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js?client=ca-pub-9453835310745500\"\n     crossorigin=\"anonymous\"><\/script>\n<ins class=\"adsbygoogle\"\n     style=\"display:block; text-align:center;\"\n     data-ad-layout=\"in-article\"\n     data-ad-format=\"fluid\"\n     data-ad-client=\"ca-pub-9453835310745500\"\n     data-ad-slot=\"6565358754\"><\/ins>\n<script>\n     (adsbygoogle = window.adsbygoogle || []).push({});\n<\/script>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":187055548,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center 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