{"id":6821,"date":"2021-10-21T19:12:07","date_gmt":"2021-10-21T13:42:07","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6821"},"modified":"2021-10-25T00:23:30","modified_gmt":"2021-10-24T18:53:30","slug":"prove-that-sin-112over-13-cot-14over-3-tan-163over-16-pi","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/prove-that-sin-112over-13-cot-14over-3-tan-163over-16-pi\/","title":{"rendered":"Prove that : \\(sin^{-1}{12\\over 13}\\) + \\(cot^{-1}{4\\over 3}\\) + \\(tan^{-1}{63\\over 16}\\) = \\(\\pi\\)"},"content":{"rendered":"

Solution :<\/h2>\n

We have, \\(sin^{-1}{12\\over 13}\\) + \\(cot^{-1}{4\\over 3}\\) + \\(tan^{-1}{63\\over 16}\\)<\/p>\n

= \\(tan^{-1}{12\\over 5}\\) + \\(tan^{-1}{3\\over 4}\\) + \\(tan^{-1}{63\\over 16}\\)<\/p>\n

= \\(\\pi\\) + \\(tan^{-1}({{{12\\over 5} + {3\\over 4}}\\over {1 – {12\\over 5} \\times {3\\over 4}}})\\) + \\(tan^{-1}{63\\over 16}\\)<\/p>\n

= \\(\\pi\\) + \\(tan^{-1}{63\\over (-16)}\\) + \\(tan^{-1}{63\\over 16}\\)<\/p>\n

= \\(\\pi\\) – \\(tan^{-1}{63\\over 16}\\) + \\(tan^{-1}{63\\over 16}\\)<\/p>\n

= \\(\\pi\\)<\/p>\n

\n

Similar Questions<\/h3>\n

Solve the equation : 2\\(tan^{-1}({2x+1})\\) = \\(cos^{-1}x\\)<\/a><\/p>\n

The value of \\(tan^{-1}(1)\\) + \\(cos^{-1}({-1\\over 2})\\) + \\(sin^{-1}({-1\\over 2})\\) is equal to<\/a><\/p>\n

Evaluate \\(sin^{-1}(sin10)\\)<\/a><\/p>\n

Prove that : \\(cos^{-1}{12\\over 13}\\) + \\(sin^{-1}{3\\over 5}\\) = \\(sin^{-1}{56\\over 65}\\)<\/a><\/p>\n

Find the value of \\(sin^{-1}({-\\sqrt{3}\\over 2})\\) + \\(cos^{-1}(cos({7\\pi\\over 6}))\\).<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : We have, \\(sin^{-1}{12\\over 13}\\) + \\(cot^{-1}{4\\over 3}\\) + \\(tan^{-1}{63\\over 16}\\) = \\(tan^{-1}{12\\over 5}\\) + \\(tan^{-1}{3\\over 4}\\) + \\(tan^{-1}{63\\over 16}\\) = \\(\\pi\\) + \\(tan^{-1}({{{12\\over 5} + {3\\over 4}}\\over {1 – {12\\over 5} \\times {3\\over 4}}})\\) + \\(tan^{-1}{63\\over 16}\\) = \\(\\pi\\) + \\(tan^{-1}{63\\over (-16)}\\) + \\(tan^{-1}{63\\over 16}\\) = \\(\\pi\\) – \\(tan^{-1}{63\\over 16}\\) + \\(tan^{-1}{63\\over 16}\\) …<\/p>\n

Prove that : \\(sin^{-1}{12\\over 13}\\) + \\(cot^{-1}{4\\over 3}\\) + \\(tan^{-1}{63\\over 16}\\) = \\(\\pi\\)<\/span> Read More »<\/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":"\nProve that : \\(sin^{-1}{12\\over 13}\\) + \\(cot^{-1}{4\\over 3}\\) + \\(tan^{-1}{63\\over 16}\\) = \\(\\pi\\)<\/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-sin-112over-13-cot-14over-3-tan-163over-16-pi\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Prove that : \\(sin^{-1}{12\\over 13}\\) + \\(cot^{-1}{4\\over 3}\\) + \\(tan^{-1}{63\\over 16}\\) = \\(\\pi\\)\" \/>\n<meta property=\"og:description\" content=\"Solution : We have, (sin^{-1}{12over 13}) + (cot^{-1}{4over 3}) + (tan^{-1}{63over 16}) = (tan^{-1}{12over 5}) + (tan^{-1}{3over 4}) + (tan^{-1}{63over 16}) = (pi) + (tan^{-1}({{{12over 5} + {3over 4}}over {1 – {12over 5} times {3over 4}}})) + (tan^{-1}{63over 16}) = (pi) + (tan^{-1}{63over (-16)}) + (tan^{-1}{63over 16}) = (pi) – (tan^{-1}{63over 16}) + (tan^{-1}{63over 16}) … Prove that : (sin^{-1}{12over 13}) + (cot^{-1}{4over 3}) + (tan^{-1}{63over 16}) = (pi) Read 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Prove that : (sin^{-1}{12over 13}) + (cot^{-1}{4over 3}) + (tan^{-1}{63over 16}) = (pi) Read More »","og_url":"https:\/\/mathemerize.com\/prove-that-sin-112over-13-cot-14over-3-tan-163over-16-pi\/","og_site_name":"Mathemerize","article_published_time":"2021-10-21T13:42:07+00:00","article_modified_time":"2021-10-24T18:53:30+00:00","author":"mathemerize","twitter_card":"summary_large_image","twitter_misc":{"Written by":"mathemerize","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathemerize.com\/prove-that-sin-112over-13-cot-14over-3-tan-163over-16-pi\/#article","isPartOf":{"@id":"https:\/\/mathemerize.com\/prove-that-sin-112over-13-cot-14over-3-tan-163over-16-pi\/"},"author":{"name":"mathemerize","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df"},"headline":"Prove that : \\(sin^{-1}{12\\over 13}\\) + \\(cot^{-1}{4\\over 3}\\) + \\(tan^{-1}{63\\over 16}\\) = 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