{"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. If A + B + C = (3piover 2), then cos2A + … Prove that (2cos2A+1over {2cos2A-1}) = tan((60^{circ}) + A)tan((60^{circ}) – A) Read More »\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathemerize.com\/prove-that-2cos2a1over-2cos2a-1-tan60circ-atan60circ-a\/\" \/>\n<meta property=\"og:site_name\" content=\"Mathemerize\" \/>\n<meta property=\"article:published_time\" content=\"2021-10-21T16:44:35+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2021-10-25T04:30:56+00:00\" \/>\n<meta name=\"author\" content=\"mathemerize\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"mathemerize\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathemerize.com\/prove-that-2cos2a1over-2cos2a-1-tan60circ-atan60circ-a\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/prove-that-2cos2a1over-2cos2a-1-tan60circ-atan60circ-a\/\"},\"author\":{\"name\":\"mathemerize\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\"},\"headline\":\"Prove that \\\\(2cos2A+1\\\\over {2cos2A-1}\\\\) = tan(\\\\(60^{\\\\circ}\\\\) + A)tan(\\\\(60^{\\\\circ}\\\\) – A)\",\"datePublished\":\"2021-10-21T16:44:35+00:00\",\"dateModified\":\"2021-10-25T04:30:56+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathemerize.com\/prove-that-2cos2a1over-2cos2a-1-tan60circ-atan60circ-a\/\"},\"wordCount\":155,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathemerize.com\/#organization\"},\"articleSection\":[\"Maths Questions\",\"Trigonometry Questions\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathemerize.com\/prove-that-2cos2a1over-2cos2a-1-tan60circ-atan60circ-a\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathemerize.com\/prove-that-2cos2a1over-2cos2a-1-tan60circ-atan60circ-a\/\",\"url\":\"https:\/\/mathemerize.com\/prove-that-2cos2a1over-2cos2a-1-tan60circ-atan60circ-a\/\",\"name\":\"Prove that \\\\(2cos2A+1\\\\over {2cos2A-1}\\\\) = tan(\\\\(60^{\\\\circ}\\\\) + A)tan(\\\\(60^{\\\\circ}\\\\) - A)\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/#website\"},\"datePublished\":\"2021-10-21T16:44:35+00:00\",\"dateModified\":\"2021-10-25T04:30:56+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/mathemerize.com\/prove-that-2cos2a1over-2cos2a-1-tan60circ-atan60circ-a\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathemerize.com\/prove-that-2cos2a1over-2cos2a-1-tan60circ-atan60circ-a\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathemerize.com\/prove-that-2cos2a1over-2cos2a-1-tan60circ-atan60circ-a\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathemerize.com\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Prove that \\\\(2cos2A+1\\\\over {2cos2A-1}\\\\) = tan(\\\\(60^{\\\\circ}\\\\) + A)tan(\\\\(60^{\\\\circ}\\\\) – A)\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mathemerize.com\/#website\",\"url\":\"https:\/\/mathemerize.com\/\",\"name\":\"Mathemerize\",\"description\":\"Maths Tutorials - Study Math Online\",\"publisher\":{\"@id\":\"https:\/\/mathemerize.com\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/mathemerize.com\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/mathemerize.com\/#organization\",\"name\":\"Mathemerize\",\"url\":\"https:\/\/mathemerize.com\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1\",\"contentUrl\":\"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1\",\"width\":140,\"height\":96,\"caption\":\"Mathemerize\"},\"image\":{\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/\"},\"sameAs\":[\"https:\/\/www.instagram.com\/mathemerize\/\"]},{\"@type\":\"Person\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\",\"name\":\"mathemerize\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g\",\"caption\":\"mathemerize\"},\"sameAs\":[\"https:\/\/mathemerize.com\"],\"url\":\"https:\/\/mathemerize.com\/author\/mathemerize\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Prove that \\(2cos2A+1\\over {2cos2A-1}\\) = tan(\\(60^{\\circ}\\) + A)tan(\\(60^{\\circ}\\) - 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. If A + B + C = (3piover 2), then cos2A + … Prove that (2cos2A+1over {2cos2A-1}) = tan((60^{circ}) + A)tan((60^{circ}) – A) Read More »","og_url":"https:\/\/mathemerize.com\/prove-that-2cos2a1over-2cos2a-1-tan60circ-atan60circ-a\/","og_site_name":"Mathemerize","article_published_time":"2021-10-21T16:44:35+00:00","article_modified_time":"2021-10-25T04:30:56+00:00","author":"mathemerize","twitter_card":"summary_large_image","twitter_misc":{"Written by":"mathemerize","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathemerize.com\/prove-that-2cos2a1over-2cos2a-1-tan60circ-atan60circ-a\/#article","isPartOf":{"@id":"https:\/\/mathemerize.com\/prove-that-2cos2a1over-2cos2a-1-tan60circ-atan60circ-a\/"},"author":{"name":"mathemerize","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df"},"headline":"Prove that \\(2cos2A+1\\over {2cos2A-1}\\) = tan(\\(60^{\\circ}\\) + A)tan(\\(60^{\\circ}\\) – A)","datePublished":"2021-10-21T16:44:35+00:00","dateModified":"2021-10-25T04:30:56+00:00","mainEntityOfPage":{"@id":"https:\/\/mathemerize.com\/prove-that-2cos2a1over-2cos2a-1-tan60circ-atan60circ-a\/"},"wordCount":155,"commentCount":0,"publisher":{"@id":"https:\/\/mathemerize.com\/#organization"},"articleSection":["Maths Questions","Trigonometry Questions"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/mathemerize.com\/prove-that-2cos2a1over-2cos2a-1-tan60circ-atan60circ-a\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/mathemerize.com\/prove-that-2cos2a1over-2cos2a-1-tan60circ-atan60circ-a\/","url":"https:\/\/mathemerize.com\/prove-that-2cos2a1over-2cos2a-1-tan60circ-atan60circ-a\/","name":"Prove that \\(2cos2A+1\\over {2cos2A-1}\\) = tan(\\(60^{\\circ}\\) + A)tan(\\(60^{\\circ}\\) - A)","isPartOf":{"@id":"https:\/\/mathemerize.com\/#website"},"datePublished":"2021-10-21T16:44:35+00:00","dateModified":"2021-10-25T04:30:56+00:00","breadcrumb":{"@id":"https:\/\/mathemerize.com\/prove-that-2cos2a1over-2cos2a-1-tan60circ-atan60circ-a\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mathemerize.com\/prove-that-2cos2a1over-2cos2a-1-tan60circ-atan60circ-a\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/mathemerize.com\/prove-that-2cos2a1over-2cos2a-1-tan60circ-atan60circ-a\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mathemerize.com\/"},{"@type":"ListItem","position":2,"name":"Prove that \\(2cos2A+1\\over {2cos2A-1}\\) = tan(\\(60^{\\circ}\\) + A)tan(\\(60^{\\circ}\\) – A)"}]},{"@type":"WebSite","@id":"https:\/\/mathemerize.com\/#website","url":"https:\/\/mathemerize.com\/","name":"Mathemerize","description":"Maths Tutorials - Study Math Online","publisher":{"@id":"https:\/\/mathemerize.com\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/mathemerize.com\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/mathemerize.com\/#organization","name":"Mathemerize","url":"https:\/\/mathemerize.com\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/","url":"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1","contentUrl":"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1","width":140,"height":96,"caption":"Mathemerize"},"image":{"@id":"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.instagram.com\/mathemerize\/"]},{"@type":"Person","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df","name":"mathemerize","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g","caption":"mathemerize"},"sameAs":["https:\/\/mathemerize.com"],"url":"https:\/\/mathemerize.com\/author\/mathemerize\/"}]}},"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/6895"}],"collection":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/comments?post=6895"}],"version-history":[{"count":2,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/6895\/revisions"}],"predecessor-version":[{"id":7535,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/6895\/revisions\/7535"}],"wp:attachment":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/media?parent=6895"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/categories?post=6895"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/tags?post=6895"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}