{"id":11724,"date":"2022-08-16T17:19:50","date_gmt":"2022-08-16T11:49:50","guid":{"rendered":"https:\/\/mathemerize.com\/?p=11724"},"modified":"2022-08-16T17:19:56","modified_gmt":"2022-08-16T11:49:56","slug":"if-a-b-and-c-are-the-interior-angles-of-a-triangle-abc-show-that-sinbcover-2-cosaover-2","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/if-a-b-and-c-are-the-interior-angles-of-a-triangle-abc-show-that-sinbcover-2-cosaover-2\/","title":{"rendered":"If A, B and C are the interior angles of a triangle ABC, show that sin\\(B+C\\over 2\\) = cos\\(A\\over 2\\)."},"content":{"rendered":"<h2>Solution :<\/h2>\n<p>Since A, B and C are the interior angles of a triangle ABC<\/p>\n<p>\\(\\therefore\\)\u00a0 \u00a0A + B + C = 180<\/p>\n<p>\\(\\implies\\)\u00a0 \\(A\\over 2\\) + \\(B\\over 2\\) + \\(C\\over 2\\) = 90<\/p>\n<p>\\(\\implies\\)\u00a0 \\(B\\over 2\\) + \\(C\\over 2\\) = 90 &#8211; \\(A\\over 2\\)<\/p>\n<p>\\(\\implies\\)\u00a0 sin(\\(B+C\\over 2\\)) = sin(90 &#8211; \\(A\\over 2\\))<\/p>\n<p>\\(\\implies\\)\u00a0 \u00a0sin\\(B+C\\over 2\\) = cos\\(A\\over 2\\).<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Solution : Since A, B and C are the interior angles of a triangle ABC \\(\\therefore\\)\u00a0 \u00a0A + B + C = 180 \\(\\implies\\)\u00a0 \\(A\\over 2\\) + \\(B\\over 2\\) + \\(C\\over 2\\) = 90 \\(\\implies\\)\u00a0 \\(B\\over 2\\) + \\(C\\over 2\\) = 90 &#8211; \\(A\\over 2\\) \\(\\implies\\)\u00a0 sin(\\(B+C\\over 2\\)) = sin(90 &#8211; \\(A\\over 2\\)) \\(\\implies\\)\u00a0 \u00a0sin\\(B+C\\over &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathemerize.com\/if-a-b-and-c-are-the-interior-angles-of-a-triangle-abc-show-that-sinbcover-2-cosaover-2\/\"> <span class=\"screen-reader-text\">If A, B and C are the interior angles of a triangle ABC, show that sin\\(B+C\\over 2\\) = cos\\(A\\over 2\\).<\/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 A, B and C are the interior angles of a triangle ABC, show that sin\\(B+C\\over 2\\) = cos\\(A\\over 2\\). - 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-a-b-and-c-are-the-interior-angles-of-a-triangle-abc-show-that-sinbcover-2-cosaover-2\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"If A, B and C are the interior angles of a triangle ABC, show that sin\\(B+C\\over 2\\) = cos\\(A\\over 2\\). - Mathemerize\" \/>\n<meta property=\"og:description\" content=\"Solution : Since A, B and C are the interior angles of a triangle ABC (therefore)\u00a0 \u00a0A + B + C = 180 (implies)\u00a0 (Aover 2) + (Bover 2) + (Cover 2) = 90 (implies)\u00a0 (Bover 2) + (Cover 2) = 90 &#8211; (Aover 2) (implies)\u00a0 sin((B+Cover 2)) = sin(90 &#8211; (Aover 2)) (implies)\u00a0 \u00a0sin(B+Cover &hellip; If A, B and C are the interior angles of a triangle ABC, show that sin(B+Cover 2) = cos(Aover 2). 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Mathemerize","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\/if-a-b-and-c-are-the-interior-angles-of-a-triangle-abc-show-that-sinbcover-2-cosaover-2\/","og_locale":"en_US","og_type":"article","og_title":"If A, B and C are the interior angles of a triangle ABC, show that sin\\(B+C\\over 2\\) = cos\\(A\\over 2\\). - Mathemerize","og_description":"Solution : Since A, B and C are the interior angles of a triangle ABC (therefore)\u00a0 \u00a0A + B + C = 180 (implies)\u00a0 (Aover 2) + (Bover 2) + (Cover 2) = 90 (implies)\u00a0 (Bover 2) + (Cover 2) = 90 &#8211; (Aover 2) (implies)\u00a0 sin((B+Cover 2)) = sin(90 &#8211; (Aover 2)) (implies)\u00a0 \u00a0sin(B+Cover &hellip; If A, B and C are the interior angles of a triangle ABC, show that sin(B+Cover 2) = cos(Aover 2). 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