{"id":6900,"date":"2021-10-21T22:16:41","date_gmt":"2021-10-21T16:46:41","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6900"},"modified":"2021-10-25T10:00:42","modified_gmt":"2021-10-25T04:30:42","slug":"if-a-b-c-3piover-2-then-cos2a-cos2b-cos2c-is-equal-to","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/if-a-b-c-3piover-2-then-cos2a-cos2b-cos2c-is-equal-to\/","title":{"rendered":"If A + B + C = \\(3\\pi\\over 2\\), then cos2A + cos2B + cos2C is equal to"},"content":{"rendered":"<h2>Solution :<\/h2>\n<p>cos2A + cos2B + cos2C = 2cos(A+B)cos(A-B) + cos2C<\/p>\n<p>= 2cos(\\(3\\pi\\over 2\\) &#8211; C)cos(A-B) + cos2C\u00a0 \\(\\because\\)\u00a0 A + B + C = \\(3\\pi\\over 2\\)<\/p>\n<p>= -2sinC cos(A-B) + 1 &#8211; 2\\(sin^2C\\) = 1 &#8211; 2sinC[cos(A-B)+sinC]<\/p>\n<p>= 1 &#8211; 2sinC[cos(A-B) + sin(\\(3\\pi\\over 2\\)-(A+B))]<\/p>\n<p>= 1 &#8211; 2sinC[cos(A-B)-cos(A+B)]<\/p>\n<p>= 1 &#8211; 4sinA sinB sinC<\/p>\n<hr \/>\n<h3 style=\"text-align: center;\">Similar Questions<\/h3>\n<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/evaluate-sin78-sin66-sin42-sin6\/\" aria-label=\"\u201cEvaluate sin78 \u2013 sin66 \u2013 sin42 + sin6.\u201d (Edit)\">Evaluate sin78 \u2013 sin66 \u2013 sin42 + sin6.<\/a><\/p>\n<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/find-the-maximum-value-of-1-sinpiover-4-theta-2cospiover-4-theta\/\" aria-label=\"\u201cFind the maximum value of 1 + \\(sin({\\pi\\over 4} + \\theta)\\) + \\(2cos({\\pi\\over 4} \u2013 \\theta)\\)\u201d (Edit)\">Find the maximum value of 1 + \\(sin({\\pi\\over 4} + \\theta)\\) + \\(2cos({\\pi\\over 4} \u2013 \\theta)\\)<\/a><\/p>\n<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/sin5x-sin2x-sinxover-cos5x-2cos3x-2cosx-cosx-is-equal-to\/\" aria-label=\"\u201c\\(sin5x + sin2x \u2013 sinx\\over {cos5x + 2cos3x + 2cos^x + cosx}\\) is equal to\u201d (Edit)\">\\(sin5x + sin2x \u2013 sinx\\over {cos5x + 2cos3x + 2cos^x + cosx}\\) is equal to<\/a><\/p>\n<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/prove-that-2cos2a1over-2cos2a-1-tan60circ-atan60circ-a\/\" aria-label=\"\u201cProve that  \\(2cos2A+1\\over {2cos2A-1}\\) = tan(\\(60^{\\circ}\\) + A)tan(\\(60^{\\circ}\\) \u2013 A)\u201d (Edit)\">Prove that \\(2cos2A+1\\over {2cos2A-1}\\) = tan(\\(60^{\\circ}\\) + A)tan(\\(60^{\\circ}\\) \u2013 A)<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Solution : cos2A + cos2B + cos2C = 2cos(A+B)cos(A-B) + cos2C = 2cos(\\(3\\pi\\over 2\\) &#8211; C)cos(A-B) + cos2C\u00a0 \\(\\because\\)\u00a0 A + B + C = \\(3\\pi\\over 2\\) = -2sinC cos(A-B) + 1 &#8211; 2\\(sin^2C\\) = 1 &#8211; 2sinC[cos(A-B)+sinC] = 1 &#8211; 2sinC[cos(A-B) + sin(\\(3\\pi\\over 2\\)-(A+B))] = 1 &#8211; 2sinC[cos(A-B)-cos(A+B)] = 1 &#8211; 4sinA sinB sinC &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathemerize.com\/if-a-b-c-3piover-2-then-cos2a-cos2b-cos2c-is-equal-to\/\"> <span class=\"screen-reader-text\">If A + B + C = \\(3\\pi\\over 2\\), then cos2A + cos2B + cos2C is equal to<\/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":[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 A + B + C = \\(3\\pi\\over 2\\), then cos2A + cos2B + cos2C is equal to<\/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-a-b-c-3piover-2-then-cos2a-cos2b-cos2c-is-equal-to\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"If A + B + C = \\(3\\pi\\over 2\\), then cos2A + cos2B + cos2C is equal to\" \/>\n<meta property=\"og:description\" content=\"Solution : cos2A + cos2B + cos2C = 2cos(A+B)cos(A-B) + cos2C = 2cos((3piover 2) &#8211; C)cos(A-B) + cos2C\u00a0 (because)\u00a0 A + B + C = (3piover 2) = -2sinC cos(A-B) + 1 &#8211; 2(sin^2C) = 1 &#8211; 2sinC[cos(A-B)+sinC] = 1 &#8211; 2sinC[cos(A-B) + sin((3piover 2)-(A+B))] = 1 &#8211; 2sinC[cos(A-B)-cos(A+B)] = 1 &#8211; 4sinA sinB sinC &hellip; If A + B + C = (3piover 2), then cos2A + cos2B + cos2C is equal to Read More &raquo;\" \/>\n<meta property=\"og:url\" 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