Prove that \\(2cos2A+1\\over {2cos2A-1}\\) = tan(\\(60^{\\circ}\\) + A)tan(\\(60^{\\circ}\\) \u2013 A)<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"Solution : We have 1 + \\(sin({\\pi\\over 4} + \\theta)\\) + \\(2cos({\\pi\\over 4} – \\theta)\\) = 1 + \\(1\\over sqrt{2}\\)\\((cos\\theta + cos\\theta)\\) + \\(\\sqrt{2}\\)\\((cos\\theta + cos\\theta)\\) = 1 + \\(({1\\over \\sqrt{2}} + \\sqrt{2})\\) + \\((cos\\theta + cos\\theta)\\) = 1 + \\(({1\\over \\sqrt{2}} + \\sqrt{2})\\).\\(\\sqrt{2}cos(\\theta – {pi\\over 4})\\) \\(\\therefore\\)\u00a0 \u00a0Maximum Value = 1 + \\(({1\\over \\sqrt{2}} …<\/p>\n
Find the maximum value of 1 + \\(sin({\\pi\\over 4} + \\theta)\\) + \\(2cos({\\pi\\over 4} – \\theta)\\)<\/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":"\nFind the maximum value of 1 + \\(sin({\\pi\\over 4} + \\theta)\\) + \\(2cos({\\pi\\over 4} - \\theta)\\)<\/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\/find-the-maximum-value-of-1-sinpiover-4-theta-2cospiover-4-theta\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Find the maximum value of 1 + \\(sin({\\pi\\over 4} + \\theta)\\) + \\(2cos({\\pi\\over 4} - \\theta)\\)\" \/>\n<meta property=\"og:description\" content=\"Solution : We have 1 + (sin({piover 4} + theta)) + (2cos({piover 4} – theta)) = 1 + (1over sqrt{2})((costheta + costheta)) + (sqrt{2})((costheta + costheta)) = 1 + (({1over sqrt{2}} + sqrt{2})) + ((costheta + costheta)) = 1 + (({1over sqrt{2}} + sqrt{2})).(sqrt{2}cos(theta – {piover 4})) (therefore)\u00a0 \u00a0Maximum Value = 1 + (({1over sqrt{2}} … Find the maximum value of 1 + (sin({piover 4} + theta)) + (2cos({piover 4} – theta)) Read More »\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathemerize.com\/find-the-maximum-value-of-1-sinpiover-4-theta-2cospiover-4-theta\/\" \/>\n<meta property=\"og:site_name\" content=\"Mathemerize\" \/>\n<meta property=\"article:published_time\" content=\"2021-10-22T20:37:37+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2021-10-25T04:29:18+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\/find-the-maximum-value-of-1-sinpiover-4-theta-2cospiover-4-theta\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/find-the-maximum-value-of-1-sinpiover-4-theta-2cospiover-4-theta\/\"},\"author\":{\"name\":\"mathemerize\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\"},\"headline\":\"Find the maximum value of 1 + \\\\(sin({\\\\pi\\\\over 4} + \\\\theta)\\\\) + \\\\(2cos({\\\\pi\\\\over 4} – \\\\theta)\\\\)\",\"datePublished\":\"2021-10-22T20:37:37+00:00\",\"dateModified\":\"2021-10-25T04:29:18+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathemerize.com\/find-the-maximum-value-of-1-sinpiover-4-theta-2cospiover-4-theta\/\"},\"wordCount\":112,\"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\/find-the-maximum-value-of-1-sinpiover-4-theta-2cospiover-4-theta\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathemerize.com\/find-the-maximum-value-of-1-sinpiover-4-theta-2cospiover-4-theta\/\",\"url\":\"https:\/\/mathemerize.com\/find-the-maximum-value-of-1-sinpiover-4-theta-2cospiover-4-theta\/\",\"name\":\"Find the maximum value of 1 + \\\\(sin({\\\\pi\\\\over 4} + \\\\theta)\\\\) + \\\\(2cos({\\\\pi\\\\over 4} - 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\\theta)\\)","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\/find-the-maximum-value-of-1-sinpiover-4-theta-2cospiover-4-theta\/","og_locale":"en_US","og_type":"article","og_title":"Find the maximum value of 1 + \\(sin({\\pi\\over 4} + \\theta)\\) + \\(2cos({\\pi\\over 4} - \\theta)\\)","og_description":"Solution : We have 1 + (sin({piover 4} + theta)) + (2cos({piover 4} – theta)) = 1 + (1over sqrt{2})((costheta + costheta)) + (sqrt{2})((costheta + costheta)) = 1 + (({1over sqrt{2}} + sqrt{2})) + ((costheta + costheta)) = 1 + (({1over sqrt{2}} + sqrt{2})).(sqrt{2}cos(theta – {piover 4})) (therefore)\u00a0 \u00a0Maximum Value = 1 + (({1over sqrt{2}} … Find the maximum value of 1 + (sin({piover 4} + theta)) + (2cos({piover 4} – theta)) Read More »","og_url":"https:\/\/mathemerize.com\/find-the-maximum-value-of-1-sinpiover-4-theta-2cospiover-4-theta\/","og_site_name":"Mathemerize","article_published_time":"2021-10-22T20:37:37+00:00","article_modified_time":"2021-10-25T04:29:18+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\/find-the-maximum-value-of-1-sinpiover-4-theta-2cospiover-4-theta\/#article","isPartOf":{"@id":"https:\/\/mathemerize.com\/find-the-maximum-value-of-1-sinpiover-4-theta-2cospiover-4-theta\/"},"author":{"name":"mathemerize","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df"},"headline":"Find the maximum value of 1 + \\(sin({\\pi\\over 4} + \\theta)\\) + \\(2cos({\\pi\\over 4} – \\theta)\\)","datePublished":"2021-10-22T20:37:37+00:00","dateModified":"2021-10-25T04:29:18+00:00","mainEntityOfPage":{"@id":"https:\/\/mathemerize.com\/find-the-maximum-value-of-1-sinpiover-4-theta-2cospiover-4-theta\/"},"wordCount":112,"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\/find-the-maximum-value-of-1-sinpiover-4-theta-2cospiover-4-theta\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/mathemerize.com\/find-the-maximum-value-of-1-sinpiover-4-theta-2cospiover-4-theta\/","url":"https:\/\/mathemerize.com\/find-the-maximum-value-of-1-sinpiover-4-theta-2cospiover-4-theta\/","name":"Find the maximum value of 1 + \\(sin({\\pi\\over 4} + \\theta)\\) + \\(2cos({\\pi\\over 4} - 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