{"id":6895,"date":"2021-10-21T22:14:35","date_gmt":"2021-10-21T16:44:35","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6895"},"modified":"2021-10-25T10:00:56","modified_gmt":"2021-10-25T04:30:56","slug":"prove-that-2cos2a1over-2cos2a-1-tan60circ-atan60circ-a","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/prove-that-2cos2a1over-2cos2a-1-tan60circ-atan60circ-a\/","title":{"rendered":"Prove that \\(2cos2A+1\\over {2cos2A-1}\\) = tan(\\(60^{\\circ}\\) + A)tan(\\(60^{\\circ}\\) – A)"},"content":{"rendered":"

Solution :<\/h2>\n

R.H.S. = tan(\\(60^{\\circ}\\) + A)tan(\\(60^{\\circ}\\) – A)<\/p>\n

= (\\(tan60^{\\circ}+tanA\\over {1-tan60^{\\circ}tanA}\\))(\\(tan60^{\\circ}-tanA\\over {1+tan60^{\\circ}tanA}\\))<\/p>\n

= (\\(\\sqrt{3}+tanA\\over {1-\\sqrt{3}tanA}\\))(\\(\\sqrt{3}-tanA\\over {1+\\sqrt{3}tanA}\\))<\/p>\n

= \\(3-tan^2A\\over{1-3tan^2A}\\) = \\(3cos^2A-sin^2A\\over {cos^2A-3sin^2A}\\)<\/p>\n

= \\(2cos^2A+cos^2A-2sin^2A+sin^2A\\over {2cos^2A-2sin^2A-sin^2A-cos^2A}\\)<\/p>\n

= \\(2(cos^2A-sin^2A)+cos^2A+sin^2A\\over {2(cos^2A-sin^2A)-(sin^2A+cos^2A)}\\)<\/p>\n

= \\(2cos2A+1\\over {2cos2A-1}\\) = L.H.S<\/p>\n


\n

Similar Questions<\/h3>\n

Evaluate sin78 \u2013 sin66 \u2013 sin42 + sin6.<\/a><\/p>\n

If A + B + C = \\(3\\pi\\over 2\\), then cos2A + cos2B + cos2C is equal to<\/a><\/p>\n

\\(sin5x + sin2x \u2013 sinx\\over {cos5x + 2cos3x + 2cos^x + cosx}\\) is equal to<\/a><\/p>\n

Find the maximum value of 1 + \\(sin({\\pi\\over 4} + \\theta)\\) + \\(2cos({\\pi\\over 4} \u2013 \\theta)\\)<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : R.H.S. = tan(\\(60^{\\circ}\\) + A)tan(\\(60^{\\circ}\\) – A) = (\\(tan60^{\\circ}+tanA\\over {1-tan60^{\\circ}tanA}\\))(\\(tan60^{\\circ}-tanA\\over {1+tan60^{\\circ}tanA}\\)) = (\\(\\sqrt{3}+tanA\\over {1-\\sqrt{3}tanA}\\))(\\(\\sqrt{3}-tanA\\over {1+\\sqrt{3}tanA}\\)) = \\(3-tan^2A\\over{1-3tan^2A}\\) = \\(3cos^2A-sin^2A\\over {cos^2A-3sin^2A}\\) = \\(2cos^2A+cos^2A-2sin^2A+sin^2A\\over {2cos^2A-2sin^2A-sin^2A-cos^2A}\\) = \\(2(cos^2A-sin^2A)+cos^2A+sin^2A\\over {2(cos^2A-sin^2A)-(sin^2A+cos^2A)}\\) = \\(2cos2A+1\\over {2cos2A-1}\\) = L.H.S Similar Questions Evaluate sin78 \u2013 sin66 \u2013 sin42 + sin6. If A + B + C = \\(3\\pi\\over 2\\), then cos2A + …<\/p>\n

Prove that \\(2cos2A+1\\over {2cos2A-1}\\) = tan(\\(60^{\\circ}\\) + A)tan(\\(60^{\\circ}\\) – A)<\/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":[43,60],"tags":[],"yoast_head":"\nProve that \\(2cos2A+1\\over {2cos2A-1}\\) = tan(\\(60^{\\circ}\\) + A)tan(\\(60^{\\circ}\\) - A)<\/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-2cos2a1over-2cos2a-1-tan60circ-atan60circ-a\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Prove that \\(2cos2A+1\\over {2cos2A-1}\\) = tan(\\(60^{\\circ}\\) + A)tan(\\(60^{\\circ}\\) - A)\" \/>\n<meta property=\"og:description\" content=\"Solution : R.H.S. = tan((60^{circ}) + A)tan((60^{circ}) – A) = ((tan60^{circ}+tanAover {1-tan60^{circ}tanA}))((tan60^{circ}-tanAover {1+tan60^{circ}tanA})) = ((sqrt{3}+tanAover {1-sqrt{3}tanA}))((sqrt{3}-tanAover {1+sqrt{3}tanA})) = (3-tan^2Aover{1-3tan^2A}) = (3cos^2A-sin^2Aover {cos^2A-3sin^2A}) = (2cos^2A+cos^2A-2sin^2A+sin^2Aover {2cos^2A-2sin^2A-sin^2A-cos^2A}) = (2(cos^2A-sin^2A)+cos^2A+sin^2Aover {2(cos^2A-sin^2A)-(sin^2A+cos^2A)}) = (2cos2A+1over {2cos2A-1}) = L.H.S Similar Questions Evaluate sin78 \u2013 sin66 \u2013 sin42 + sin6. 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A)","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\/prove-that-2cos2a1over-2cos2a-1-tan60circ-atan60circ-a\/","og_locale":"en_US","og_type":"article","og_title":"Prove that \\(2cos2A+1\\over {2cos2A-1}\\) = tan(\\(60^{\\circ}\\) + A)tan(\\(60^{\\circ}\\) - A)","og_description":"Solution : R.H.S. = tan((60^{circ}) + A)tan((60^{circ}) – A) = ((tan60^{circ}+tanAover {1-tan60^{circ}tanA}))((tan60^{circ}-tanAover {1+tan60^{circ}tanA})) = ((sqrt{3}+tanAover {1-sqrt{3}tanA}))((sqrt{3}-tanAover {1+sqrt{3}tanA})) = (3-tan^2Aover{1-3tan^2A}) = (3cos^2A-sin^2Aover {cos^2A-3sin^2A}) = (2cos^2A+cos^2A-2sin^2A+sin^2Aover {2cos^2A-2sin^2A-sin^2A-cos^2A}) = (2(cos^2A-sin^2A)+cos^2A+sin^2Aover {2(cos^2A-sin^2A)-(sin^2A+cos^2A)}) = (2cos2A+1over {2cos2A-1}) = L.H.S Similar Questions Evaluate sin78 \u2013 sin66 \u2013 sin42 + sin6. 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