{"id":11672,"date":"2022-08-14T01:42:46","date_gmt":"2022-08-13T20:12:46","guid":{"rendered":"https:\/\/mathemerize.com\/?p=11672"},"modified":"2022-08-14T01:42:53","modified_gmt":"2022-08-13T20:12:53","slug":"if-3-cot-a-4-check-whether-1-tan2aover-1-tan2a-cos2a-sin2a-or-not","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/if-3-cot-a-4-check-whether-1-tan2aover-1-tan2a-cos2a-sin2a-or-not\/","title":{"rendered":"If 3 cot A = 4, check whether \\(1 &#8211; tan^2A\\over 1 + tan^2A\\) = \\(cos^2A &#8211; sin^2A\\) or not."},"content":{"rendered":"<h2>Solution :<\/h2>\n<p>We have,\u00a0 \u00a03 cot A = 4\u00a0 \u00a0 \\(\\implies\\)\u00a0 cot A = \\(4\\over 3\\) = \\(AB\\over BC\\)\u00a0<img decoding=\"async\" loading=\"lazy\" class=\" wp-image-11684 alignright\" src=\"https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/08\/trigonometry8-1-8-1.jpeg?resize=248%2C217&#038;ssl=1\" alt=\"\" width=\"248\" height=\"217\" srcset=\"https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/08\/trigonometry8-1-8-1.jpeg?resize=300%2C263&amp;ssl=1 300w, https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/08\/trigonometry8-1-8-1.jpeg?resize=1024%2C898&amp;ssl=1 1024w, https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/08\/trigonometry8-1-8-1.jpeg?resize=768%2C673&amp;ssl=1 768w, https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/08\/trigonometry8-1-8-1.jpeg?resize=1536%2C1346&amp;ssl=1 1536w, https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/08\/trigonometry8-1-8-1.jpeg?w=1700&amp;ssl=1 1700w\" sizes=\"(max-width: 248px) 100vw, 248px\" data-recalc-dims=\"1\" \/><\/p>\n<p>Let\u00a0 AB = 4k, then BC = 3k<\/p>\n<p>By Pythagoras Theorem,<\/p>\n<p>\\({AC}^2\\) = \\({AB}^2\\) + \\({BC}^2\\)<\/p>\n<p>\\(\\implies\\)\u00a0 \\({AC}^2\\) = \\(25k^2\\)<\/p>\n<p>\\(\\implies\\)\u00a0 AC = 5k<\/p>\n<p>Thus,\u00a0 tan A = \\(BC\\over AB\\) = \\(3k\\over 4k\\) = \\(3\\over 4\\)<\/p>\n<p>sin A = \\(BC\\over AC\\) = \\(3k\\over 5k\\) = \\(3\\over 5\\)<\/p>\n<p>cos A = \\(AB\\over AC\\) = \\(4k\\over 5k\\) = \\(4\\over 5\\)<\/p>\n<p>Now, \\(1 &#8211; tan^2A\\over 1 + tan^2A\\) = \\(16 &#8211; 9\\over 16 + 9\\) = \\(7\\over 25\\)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0&#8230;&#8230;&#8230;&#8230;(1)<\/p>\n<p>and\u00a0 \\(cos^2A &#8211; sin^2A\\) = \\(7\\over 25\\)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 &#8230;&#8230;&#8230;&#8230;.(2)<\/p>\n<p>From (1) and (2), we have :<\/p>\n<p><strong>\\(1 &#8211; tan^2A\\over 1 + tan^2A\\) = \\(cos^2A &#8211; sin^2A\\)<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Solution : We have,\u00a0 \u00a03 cot A = 4\u00a0 \u00a0 \\(\\implies\\)\u00a0 cot A = \\(4\\over 3\\) = \\(AB\\over BC\\)\u00a0 Let\u00a0 AB = 4k, then BC = 3k By Pythagoras Theorem, \\({AC}^2\\) = \\({AB}^2\\) + \\({BC}^2\\) \\(\\implies\\)\u00a0 \\({AC}^2\\) = \\(25k^2\\) \\(\\implies\\)\u00a0 AC = 5k Thus,\u00a0 tan A = \\(BC\\over AB\\) = \\(3k\\over 4k\\) = \\(3\\over 4\\) &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathemerize.com\/if-3-cot-a-4-check-whether-1-tan2aover-1-tan2a-cos2a-sin2a-or-not\/\"> <span class=\"screen-reader-text\">If 3 cot A = 4, check whether \\(1 &#8211; tan^2A\\over 1 + tan^2A\\) = \\(cos^2A &#8211; sin^2A\\) or not.<\/span> Read More &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","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":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[43,60],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.12 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>If 3 cot A = 4, check whether \\(1 - tan^2A\\over 1 + tan^2A\\) = \\(cos^2A - sin^2A\\) or not. - Mathemerize<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/if-3-cot-a-4-check-whether-1-tan2aover-1-tan2a-cos2a-sin2a-or-not\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"If 3 cot A = 4, check whether \\(1 - tan^2A\\over 1 + tan^2A\\) = \\(cos^2A - sin^2A\\) or not. - Mathemerize\" \/>\n<meta property=\"og:description\" content=\"Solution : We have,\u00a0 \u00a03 cot A = 4\u00a0 \u00a0 (implies)\u00a0 cot A = (4over 3) = (ABover BC)\u00a0 Let\u00a0 AB = 4k, then BC = 3k By Pythagoras Theorem, ({AC}^2) = ({AB}^2) + ({BC}^2) (implies)\u00a0 ({AC}^2) = (25k^2) (implies)\u00a0 AC = 5k Thus,\u00a0 tan A = (BCover AB) = (3kover 4k) = (3over 4) &hellip; 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If 3 cot A = 4, check whether (1 &#8211; tan^2Aover 1 + tan^2A) = (cos^2A &#8211; sin^2A) or not. 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