{"id":7211,"date":"2021-10-23T01:59:21","date_gmt":"2021-10-22T20:29:21","guid":{"rendered":"https:\/\/mathemerize.com\/?p=7211"},"modified":"2021-10-25T10:00:38","modified_gmt":"2021-10-25T04:30:38","slug":"evaluate-sin78-sin66-sin42-sin6","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/evaluate-sin78-sin66-sin42-sin6\/","title":{"rendered":"Evaluate sin78 &#8211; sin66 &#8211; sin42 + sin6."},"content":{"rendered":"<h2>Solution :<\/h2>\n<p>The expression = (sin78 &#8211; sin42) &#8211; (sin66 &#8211; sin6)<\/p>\n<p>= 2cos(60)sin(18) &#8211; 2cos36.sin30<\/p>\n<p>= sin18 &#8211; cos36<\/p>\n<p>= \\(({\\sqrt{5} &#8211; 1\\over 4})\\) &#8211; \\(({\\sqrt{5} + 1\\over 4})\\) = -\\(1\\over 2\\)<\/p>\n<hr \/>\n<h3 style=\"text-align: center;\">Similar Questions<\/h3>\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\/if-a-b-c-3piover-2-then-cos2a-cos2b-cos2c-is-equal-to\/\" aria-label=\"\u201cIf A + B + C = \\(3\\pi\\over 2\\), then cos2A + cos2B + cos2C is equal to\u201d (Edit)\">If A + B + C = \\(3\\pi\\over 2\\), then cos2A + cos2B + cos2C is equal to<\/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 : The expression = (sin78 &#8211; sin42) &#8211; (sin66 &#8211; sin6) = 2cos(60)sin(18) &#8211; 2cos36.sin30 = sin18 &#8211; cos36 = \\(({\\sqrt{5} &#8211; 1\\over 4})\\) &#8211; \\(({\\sqrt{5} + 1\\over 4})\\) = -\\(1\\over 2\\) Similar Questions Find the maximum value of 1 + \\(sin({\\pi\\over 4} + \\theta)\\) + \\(2cos({\\pi\\over 4} \u2013 \\theta)\\) If A + B &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathemerize.com\/evaluate-sin78-sin66-sin42-sin6\/\"> <span class=\"screen-reader-text\">Evaluate sin78 &#8211; sin66 &#8211; sin42 + sin6.<\/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>Evaluate sin78 - sin66 - sin42 + sin6.<\/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\/evaluate-sin78-sin66-sin42-sin6\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Evaluate sin78 - sin66 - sin42 + sin6.\" \/>\n<meta property=\"og:description\" content=\"Solution : The expression = (sin78 &#8211; sin42) &#8211; (sin66 &#8211; sin6) = 2cos(60)sin(18) &#8211; 2cos36.sin30 = sin18 &#8211; cos36 = (({sqrt{5} &#8211; 1over 4})) &#8211; (({sqrt{5} + 1over 4})) = -(1over 2) Similar Questions Find the maximum value of 1 + (sin({piover 4} + theta)) + (2cos({piover 4} \u2013 theta)) If A + B &hellip; Evaluate sin78 &#8211; sin66 &#8211; sin42 + sin6. 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sin42) &#8211; (sin66 &#8211; sin6) = 2cos(60)sin(18) &#8211; 2cos36.sin30 = sin18 &#8211; cos36 = (({sqrt{5} &#8211; 1over 4})) &#8211; (({sqrt{5} + 1over 4})) = -(1over 2) Similar Questions Find the maximum value of 1 + (sin({piover 4} + theta)) + (2cos({piover 4} \u2013 theta)) If A + B &hellip; Evaluate sin78 &#8211; sin66 &#8211; sin42 + sin6. 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