{"id":6817,"date":"2021-10-21T19:05:58","date_gmt":"2021-10-21T13:35:58","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6817"},"modified":"2021-10-25T00:23:26","modified_gmt":"2021-10-24T18:53:26","slug":"prove-that-cos-112over-13-sin-13over-5-sin-156over-65","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/prove-that-cos-112over-13-sin-13over-5-sin-156over-65\/","title":{"rendered":"Prove that : \\(cos^{-1}{12\\over 13}\\) + \\(sin^{-1}{3\\over 5}\\) = \\(sin^{-1}{56\\over 65}\\)"},"content":{"rendered":"<h2>Solution :<\/h2>\n<p>We have, L.H.S. = \\(cos^{-1}{12\\over 13}\\) + \\(sin^{-1}{3\\over 5}\\) = \\(tan^{-1}{5\\over 12}\\) + \\(tan^{-1}{3\\over 4}\\)<\/p>\n<p>\\(\\because\\) [ \\(cos^{-1}{12\\over 13}\\) = \\(tan^{-1}{5\\over 12}\\) &amp; \\(sin^{-1}{3\\over 5}\\) = \\(tan^{-1}{3\\over 4}\\) ]<\/p>\n<p>L.H.S. = \\(tan^{-1}({{{5\\over 12} + {3\\over 4}}\\over {1 &#8211; {5\\over 12}.{3\\over 4}}})\\) = \\(tan^{-1}{56\\over 33}\\)<\/p>\n<p>R.H.S. = \\(sin^{-1}{56\\over 65}\\) = \\(tan^{-1}{56\\over 33}\\)<\/p>\n<p>L.H.S = R.H.S.\u00a0 Hence Proved.<\/p>\n<hr \/>\n<h3 style=\"text-align: center;\">Similar Questions<\/h3>\n<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/solve-the-equation-2tan-12x1-cos-1x\/\" aria-label=\"\u201cSolve the equation : 2\\(tan^{-1}({2x+1})\\) = \\(cos^{-1}x\\)\u201d (Edit)\">Solve the equation : 2\\(tan^{-1}({2x+1})\\) = \\(cos^{-1}x\\)<\/a><\/p>\n<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/prove-that-sin-112over-13-cot-14over-3-tan-163over-16-pi\/\" aria-label=\"\u201cProve that : \\(sin^{-1}{12\\over 13}\\) + \\(cot^{-1}{4\\over 3}\\) + \\(tan^{-1}{63\\over 16}\\) = \\(\\pi\\)\u201d (Edit)\">Prove that : \\(sin^{-1}{12\\over 13}\\) + \\(cot^{-1}{4\\over 3}\\) + \\(tan^{-1}{63\\over 16}\\) = \\(\\pi\\)<\/a><\/p>\n<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/evaluate-sin-1sin10\/\" aria-label=\"\u201cEvaluate \\(sin^{-1}(sin10)\\)\u201d (Edit)\">Evaluate \\(sin^{-1}(sin10)\\)<\/a><\/p>\n<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/the-value-of-tan-11-cos-1-1over-2-sin-1-1over-2-is-equal-to\/\" aria-label=\"\u201cThe value of \\(tan^{-1}(1)\\) +  \\(cos^{-1}({-1\\over 2})\\) +  \\(sin^{-1}({-1\\over 2})\\) is equal to\u201d (Edit)\">The value of \\(tan^{-1}(1)\\) + \\(cos^{-1}({-1\\over 2})\\) + \\(sin^{-1}({-1\\over 2})\\) is equal to<\/a><\/p>\n<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/find-the-value-of-sin-1-sqrt3over-2-cos-1cos7piover-6\/\" aria-label=\"\u201cFind the value of \\(sin^{-1}({-\\sqrt{3}\\over 2})\\) + \\(cos^{-1}(cos({7\\pi\\over 6}))\\).\u201d (Edit)\">Find the value of \\(sin^{-1}({-\\sqrt{3}\\over 2})\\) + \\(cos^{-1}(cos({7\\pi\\over 6}))\\).<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Solution : We have, L.H.S. = \\(cos^{-1}{12\\over 13}\\) + \\(sin^{-1}{3\\over 5}\\) = \\(tan^{-1}{5\\over 12}\\) + \\(tan^{-1}{3\\over 4}\\) \\(\\because\\) [ \\(cos^{-1}{12\\over 13}\\) = \\(tan^{-1}{5\\over 12}\\) &amp; \\(sin^{-1}{3\\over 5}\\) = \\(tan^{-1}{3\\over 4}\\) ] L.H.S. = \\(tan^{-1}({{{5\\over 12} + {3\\over 4}}\\over {1 &#8211; {5\\over 12}.{3\\over 4}}})\\) = \\(tan^{-1}{56\\over 33}\\) R.H.S. = \\(sin^{-1}{56\\over 65}\\) = \\(tan^{-1}{56\\over 33}\\) L.H.S = &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathemerize.com\/prove-that-cos-112over-13-sin-13over-5-sin-156over-65\/\"> <span class=\"screen-reader-text\">Prove that : \\(cos^{-1}{12\\over 13}\\) + \\(sin^{-1}{3\\over 5}\\) = \\(sin^{-1}{56\\over 65}\\)<\/span> Read More &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","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":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[53,43],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.12 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Prove that : \\(cos^{-1}{12\\over 13}\\) + \\(sin^{-1}{3\\over 5}\\) = \\(sin^{-1}{56\\over 65}\\)<\/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\/prove-that-cos-112over-13-sin-13over-5-sin-156over-65\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Prove that : \\(cos^{-1}{12\\over 13}\\) + \\(sin^{-1}{3\\over 5}\\) = \\(sin^{-1}{56\\over 65}\\)\" \/>\n<meta property=\"og:description\" content=\"Solution : We have, L.H.S. = (cos^{-1}{12over 13}) + (sin^{-1}{3over 5}) = (tan^{-1}{5over 12}) + (tan^{-1}{3over 4}) (because) [ (cos^{-1}{12over 13}) = (tan^{-1}{5over 12}) &amp; (sin^{-1}{3over 5}) = (tan^{-1}{3over 4}) ] L.H.S. = (tan^{-1}({{{5over 12} + {3over 4}}over {1 &#8211; {5over 12}.{3over 4}}})) = (tan^{-1}{56over 33}) R.H.S. = (sin^{-1}{56over 65}) = (tan^{-1}{56over 33}) L.H.S = &hellip; Prove that : (cos^{-1}{12over 13}) + (sin^{-1}{3over 5}) = (sin^{-1}{56over 65}) Read More &raquo;\" \/>\n<meta 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\/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Prove that : \\(cos^{-1}{12\\over 13}\\) + \\(sin^{-1}{3\\over 5}\\) = \\(sin^{-1}{56\\over 65}\\)","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/mathemerize.com\/prove-that-cos-112over-13-sin-13over-5-sin-156over-65\/","og_locale":"en_US","og_type":"article","og_title":"Prove that : \\(cos^{-1}{12\\over 13}\\) + \\(sin^{-1}{3\\over 5}\\) = \\(sin^{-1}{56\\over 65}\\)","og_description":"Solution : We have, L.H.S. = (cos^{-1}{12over 13}) + (sin^{-1}{3over 5}) = (tan^{-1}{5over 12}) + (tan^{-1}{3over 4}) (because) [ (cos^{-1}{12over 13}) = (tan^{-1}{5over 12}) &amp; (sin^{-1}{3over 5}) = (tan^{-1}{3over 4}) ] L.H.S. = (tan^{-1}({{{5over 12} + {3over 4}}over {1 &#8211; {5over 12}.{3over 4}}})) = (tan^{-1}{56over 33}) R.H.S. = (sin^{-1}{56over 65}) = (tan^{-1}{56over 33}) L.H.S = &hellip; Prove 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