{"id":7203,"date":"2021-10-23T01:28:47","date_gmt":"2021-10-22T19:58:47","guid":{"rendered":"https:\/\/mathemerize.com\/?p=7203"},"modified":"2021-10-25T09:56:25","modified_gmt":"2021-10-25T04:26:25","slug":"if-1over-6sintheta-costheta-and-tantheta-are-in-g-p-then-the-general-solution-for-theta-is","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/if-1over-6sintheta-costheta-and-tantheta-are-in-g-p-then-the-general-solution-for-theta-is\/","title":{"rendered":"If \\({1\\over 6}sin\\theta\\), \\(cos\\theta\\) and \\(tan\\theta\\) are in G.P. then the general solution for \\(\\theta\\) is"},"content":{"rendered":"

Solution :<\/h2>\n

Since, \\({1\\over 6}sin\\theta\\), \\(cos\\theta\\) and \\(tan\\theta\\) are in G.P.<\/p>\n

\\(\\implies\\) \\(cos^2\\theta\\) = \\({1\\over 6}sin\\theta\\).\\(cos\\theta\\)<\/p>\n

\\(\\implies\\) \\(6cos^3\\theta\\) + \\(cos^2\\theta\\) – 1 = 0<\/p>\n

\\(\\therefore\\)\u00a0 \u00a0(\\(2cos\\theta – 1\\))(\\(3cos^2\\theta\\) + \\(2cos\\theta\\) + 1) = 0<\/p>\n

\\(cos\\theta\\) = \\(1\\over 2\\)\u00a0 \u00a0 \u00a0 \u00a0(other values are imaginary)<\/p>\n

\\(cos\\theta\\) = \\(cos\\pi\\over 3\\)\u00a0\u00a0<\/p>\n

\\(\\theta\\) = \\(2n\\pi \\pm {\\pi\\over 3}\\),\u00a0 n \\(\\in\\) I<\/p>\n

\n

Similar Questions<\/h3>\n

Find the number of solutions of tanx + secx = 2cosx in [0, \\(2\\pi\\)].<\/a><\/p>\n

Solve : cos3x + sin2x \u2013 sin4x = 0<\/a><\/p>\n

Solve : 6 \u2013 10cosx = 3\\(sin^2x\\)<\/a><\/p>\n

Find general solution of (2sinx \u2013 cosx)(1 + cosx) = \\(sin^2x\\)<\/a><\/p>\n\n\n

<\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : Since, \\({1\\over 6}sin\\theta\\), \\(cos\\theta\\) and \\(tan\\theta\\) are in G.P. \\(\\implies\\) \\(cos^2\\theta\\) = \\({1\\over 6}sin\\theta\\).\\(cos\\theta\\) \\(\\implies\\) \\(6cos^3\\theta\\) + \\(cos^2\\theta\\) – 1 = 0 \\(\\therefore\\)\u00a0 \u00a0(\\(2cos\\theta – 1\\))(\\(3cos^2\\theta\\) + \\(2cos\\theta\\) + 1) = 0 \\(cos\\theta\\) = \\(1\\over 2\\)\u00a0 \u00a0 \u00a0 \u00a0(other values are imaginary) \\(cos\\theta\\) = \\(cos\\pi\\over 3\\)\u00a0\u00a0 \\(\\theta\\) = \\(2n\\pi \\pm {\\pi\\over 3}\\),\u00a0 n …<\/p>\n

If \\({1\\over 6}sin\\theta\\), \\(cos\\theta\\) and \\(tan\\theta\\) are in G.P. then the general solution for \\(\\theta\\) is<\/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":[43,59],"tags":[],"yoast_head":"\nIf \\({1\\over 6}sin\\theta\\), \\(cos\\theta\\) and \\(tan\\theta\\) are in G.P. then the general solution for \\(\\theta\\) is<\/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-1over-6sintheta-costheta-and-tantheta-are-in-g-p-then-the-general-solution-for-theta-is\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"If \\({1\\over 6}sin\\theta\\), \\(cos\\theta\\) and \\(tan\\theta\\) are in G.P. then the general solution for \\(\\theta\\) is\" \/>\n<meta property=\"og:description\" content=\"Solution : Since, ({1over 6}sintheta), (costheta) and (tantheta) are in G.P. (implies) (cos^2theta) = ({1over 6}sintheta).(costheta) (implies) (6cos^3theta) + (cos^2theta) – 1 = 0 (therefore)\u00a0 \u00a0((2costheta – 1))((3cos^2theta) + (2costheta) + 1) = 0 (costheta) = (1over 2)\u00a0 \u00a0 \u00a0 \u00a0(other values are imaginary) (costheta) = (cospiover 3)\u00a0\u00a0 (theta) = (2npi pm {piover 3}),\u00a0 n … If ({1over 6}sintheta), (costheta) and (tantheta) are in G.P. then the general solution for (theta) is Read More »\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathemerize.com\/if-1over-6sintheta-costheta-and-tantheta-are-in-g-p-then-the-general-solution-for-theta-is\/\" \/>\n<meta property=\"og:site_name\" content=\"Mathemerize\" \/>\n<meta property=\"article:published_time\" content=\"2021-10-22T19:58:47+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2021-10-25T04:26:25+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\/if-1over-6sintheta-costheta-and-tantheta-are-in-g-p-then-the-general-solution-for-theta-is\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/if-1over-6sintheta-costheta-and-tantheta-are-in-g-p-then-the-general-solution-for-theta-is\/\"},\"author\":{\"name\":\"mathemerize\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\"},\"headline\":\"If \\\\({1\\\\over 6}sin\\\\theta\\\\), \\\\(cos\\\\theta\\\\) and \\\\(tan\\\\theta\\\\) are in G.P. then the general solution for \\\\(\\\\theta\\\\) is\",\"datePublished\":\"2021-10-22T19:58:47+00:00\",\"dateModified\":\"2021-10-25T04:26:25+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathemerize.com\/if-1over-6sintheta-costheta-and-tantheta-are-in-g-p-then-the-general-solution-for-theta-is\/\"},\"wordCount\":110,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathemerize.com\/#organization\"},\"articleSection\":[\"Maths Questions\",\"Trigonometric Equations Questions\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathemerize.com\/if-1over-6sintheta-costheta-and-tantheta-are-in-g-p-then-the-general-solution-for-theta-is\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathemerize.com\/if-1over-6sintheta-costheta-and-tantheta-are-in-g-p-then-the-general-solution-for-theta-is\/\",\"url\":\"https:\/\/mathemerize.com\/if-1over-6sintheta-costheta-and-tantheta-are-in-g-p-then-the-general-solution-for-theta-is\/\",\"name\":\"If \\\\({1\\\\over 6}sin\\\\theta\\\\), \\\\(cos\\\\theta\\\\) and \\\\(tan\\\\theta\\\\) are in G.P. then the general solution for \\\\(\\\\theta\\\\) is\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/#website\"},\"datePublished\":\"2021-10-22T19:58:47+00:00\",\"dateModified\":\"2021-10-25T04:26:25+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/mathemerize.com\/if-1over-6sintheta-costheta-and-tantheta-are-in-g-p-then-the-general-solution-for-theta-is\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathemerize.com\/if-1over-6sintheta-costheta-and-tantheta-are-in-g-p-then-the-general-solution-for-theta-is\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathemerize.com\/if-1over-6sintheta-costheta-and-tantheta-are-in-g-p-then-the-general-solution-for-theta-is\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathemerize.com\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"If \\\\({1\\\\over 6}sin\\\\theta\\\\), \\\\(cos\\\\theta\\\\) and \\\\(tan\\\\theta\\\\) are in G.P. then the general solution for \\\\(\\\\theta\\\\) is\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mathemerize.com\/#website\",\"url\":\"https:\/\/mathemerize.com\/\",\"name\":\"Mathemerize\",\"description\":\"Maths Tutorials - 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(implies) (cos^2theta) = ({1over 6}sintheta).(costheta) (implies) (6cos^3theta) + (cos^2theta) – 1 = 0 (therefore)\u00a0 \u00a0((2costheta – 1))((3cos^2theta) + (2costheta) + 1) = 0 (costheta) = (1over 2)\u00a0 \u00a0 \u00a0 \u00a0(other values are imaginary) (costheta) = (cospiover 3)\u00a0\u00a0 (theta) = (2npi pm {piover 3}),\u00a0 n … If ({1over 6}sintheta), (costheta) and (tantheta) are in G.P. then the general solution for (theta) is Read More »","og_url":"https:\/\/mathemerize.com\/if-1over-6sintheta-costheta-and-tantheta-are-in-g-p-then-the-general-solution-for-theta-is\/","og_site_name":"Mathemerize","article_published_time":"2021-10-22T19:58:47+00:00","article_modified_time":"2021-10-25T04:26:25+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\/if-1over-6sintheta-costheta-and-tantheta-are-in-g-p-then-the-general-solution-for-theta-is\/#article","isPartOf":{"@id":"https:\/\/mathemerize.com\/if-1over-6sintheta-costheta-and-tantheta-are-in-g-p-then-the-general-solution-for-theta-is\/"},"author":{"name":"mathemerize","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df"},"headline":"If \\({1\\over 6}sin\\theta\\), \\(cos\\theta\\) and \\(tan\\theta\\) are in G.P. then the general solution for \\(\\theta\\) is","datePublished":"2021-10-22T19:58:47+00:00","dateModified":"2021-10-25T04:26:25+00:00","mainEntityOfPage":{"@id":"https:\/\/mathemerize.com\/if-1over-6sintheta-costheta-and-tantheta-are-in-g-p-then-the-general-solution-for-theta-is\/"},"wordCount":110,"commentCount":0,"publisher":{"@id":"https:\/\/mathemerize.com\/#organization"},"articleSection":["Maths Questions","Trigonometric Equations Questions"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/mathemerize.com\/if-1over-6sintheta-costheta-and-tantheta-are-in-g-p-then-the-general-solution-for-theta-is\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/mathemerize.com\/if-1over-6sintheta-costheta-and-tantheta-are-in-g-p-then-the-general-solution-for-theta-is\/","url":"https:\/\/mathemerize.com\/if-1over-6sintheta-costheta-and-tantheta-are-in-g-p-then-the-general-solution-for-theta-is\/","name":"If \\({1\\over 6}sin\\theta\\), \\(cos\\theta\\) and \\(tan\\theta\\) are in G.P. then the general solution for \\(\\theta\\) is","isPartOf":{"@id":"https:\/\/mathemerize.com\/#website"},"datePublished":"2021-10-22T19:58:47+00:00","dateModified":"2021-10-25T04:26:25+00:00","breadcrumb":{"@id":"https:\/\/mathemerize.com\/if-1over-6sintheta-costheta-and-tantheta-are-in-g-p-then-the-general-solution-for-theta-is\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mathemerize.com\/if-1over-6sintheta-costheta-and-tantheta-are-in-g-p-then-the-general-solution-for-theta-is\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/mathemerize.com\/if-1over-6sintheta-costheta-and-tantheta-are-in-g-p-then-the-general-solution-for-theta-is\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mathemerize.com\/"},{"@type":"ListItem","position":2,"name":"If \\({1\\over 6}sin\\theta\\), \\(cos\\theta\\) and \\(tan\\theta\\) are in G.P. then the general solution for \\(\\theta\\) is"}]},{"@type":"WebSite","@id":"https:\/\/mathemerize.com\/#website","url":"https:\/\/mathemerize.com\/","name":"Mathemerize","description":"Maths Tutorials - 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