{"id":6815,"date":"2021-10-21T18:59:21","date_gmt":"2021-10-21T13:29:21","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6815"},"modified":"2021-10-25T00:23:20","modified_gmt":"2021-10-24T18:53:20","slug":"find-the-value-of-sin-1-sqrt3over-2-cos-1cos7piover-6","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/find-the-value-of-sin-1-sqrt3over-2-cos-1cos7piover-6\/","title":{"rendered":"Find the value of \\(sin^{-1}({-\\sqrt{3}\\over 2})\\) + \\(cos^{-1}(cos({7\\pi\\over 6}))\\)."},"content":{"rendered":"<h2>Solution :<\/h2>\n<p>\\(sin^{-1}({-\\sqrt{3}\\over 2})\\) = &#8211; \\(sin^{-1}({\\sqrt{3}\\over 2})\\) = \\(-\\pi\\over 3\\)<\/p>\n<p>\\(cos^{-1}(cos({7\\pi\\over 6}))\\) = \\(cos^{-1}(cos({2\\pi &#8211; {5\\pi\\over 6}}))\\) = \\(cos^{-1}(cos({5\\pi\\over 6}))\\) = \\(5\\pi\\over 6\\)<\/p>\n<p>Hence \\(sin^{-1}({-\\sqrt{3}\\over 2})\\) + \\(cos^{-1}(cos({7\\pi\\over 6}))\\) = \\(-\\pi\\over 3\\) + \\(5\\pi\\over 6\\) = \\(\\pi\\over 2\\)<\/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\/prove-that-cos-112over-13-sin-13over-5-sin-156over-65\/\" aria-label=\"\u201cProve that : \\(cos^{-1}{12\\over 13}\\) + \\(sin^{-1}{3\\over 5}\\) = \\(sin^{-1}{56\\over 65}\\)\u201d (Edit)\">Prove that : \\(cos^{-1}{12\\over 13}\\) + \\(sin^{-1}{3\\over 5}\\) = \\(sin^{-1}{56\\over 65}\\)<\/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","protected":false},"excerpt":{"rendered":"<p>Solution : \\(sin^{-1}({-\\sqrt{3}\\over 2})\\) = &#8211; \\(sin^{-1}({\\sqrt{3}\\over 2})\\) = \\(-\\pi\\over 3\\) \\(cos^{-1}(cos({7\\pi\\over 6}))\\) = \\(cos^{-1}(cos({2\\pi &#8211; {5\\pi\\over 6}}))\\) = \\(cos^{-1}(cos({5\\pi\\over 6}))\\) = \\(5\\pi\\over 6\\) Hence \\(sin^{-1}({-\\sqrt{3}\\over 2})\\) + \\(cos^{-1}(cos({7\\pi\\over 6}))\\) = \\(-\\pi\\over 3\\) + \\(5\\pi\\over 6\\) = \\(\\pi\\over 2\\) Similar Questions Solve the equation : 2\\(tan^{-1}({2x+1})\\) = \\(cos^{-1}x\\) Prove that : \\(sin^{-1}{12\\over 13}\\) + \\(cot^{-1}{4\\over &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathemerize.com\/find-the-value-of-sin-1-sqrt3over-2-cos-1cos7piover-6\/\"> <span class=\"screen-reader-text\">Find the value of \\(sin^{-1}({-\\sqrt{3}\\over 2})\\) + \\(cos^{-1}(cos({7\\pi\\over 6}))\\).<\/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":"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>Find the value of \\(sin^{-1}({-\\sqrt{3}\\over 2})\\) + \\(cos^{-1}(cos({7\\pi\\over 6}))\\).<\/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\/find-the-value-of-sin-1-sqrt3over-2-cos-1cos7piover-6\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Find the value of \\(sin^{-1}({-\\sqrt{3}\\over 2})\\) + \\(cos^{-1}(cos({7\\pi\\over 6}))\\).\" \/>\n<meta property=\"og:description\" content=\"Solution : (sin^{-1}({-sqrt{3}over 2})) = &#8211; (sin^{-1}({sqrt{3}over 2})) = (-piover 3) (cos^{-1}(cos({7piover 6}))) = (cos^{-1}(cos({2pi &#8211; {5piover 6}}))) = (cos^{-1}(cos({5piover 6}))) = (5piover 6) Hence (sin^{-1}({-sqrt{3}over 2})) + (cos^{-1}(cos({7piover 6}))) = (-piover 3) + (5piover 6) = (piover 2) Similar Questions Solve the equation : 2(tan^{-1}({2x+1})) = (cos^{-1}x) Prove that : (sin^{-1}{12over 13}) + (cot^{-1}{4over &hellip; Find the value of (sin^{-1}({-sqrt{3}over 2})) + (cos^{-1}(cos({7piover 6}))). 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