{"id":7205,"date":"2021-10-23T01:36:49","date_gmt":"2021-10-22T20:06:49","guid":{"rendered":"https:\/\/mathemerize.com\/?p=7205"},"modified":"2021-10-25T09:55:07","modified_gmt":"2021-10-25T04:25:07","slug":"find-the-number-of-solutions-of-tanx-secx-2cosx-in-0-2pi","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/find-the-number-of-solutions-of-tanx-secx-2cosx-in-0-2pi\/","title":{"rendered":"Find the number of solutions of tanx + secx = 2cosx in [0, \\(2\\pi\\)]."},"content":{"rendered":"

Solution :<\/h2>\n

Here, tanx + secx = 2cosx\u00a0 \u00a0 \u00a0 \u00a0\\(\\implies\\)\u00a0 \u00a0 \u00a0sinx + 1 = \\(2cos^2x\\)<\/p>\n

\\(\\implies\\) \\(2sin^2x\\) + sinx – 1 = 0\u00a0 \u00a0 \u00a0\\(\\implies\\)\u00a0 \u00a0 sinx = \\(1\\over 2\\), -1<\/p>\n

But sinx = -1 \\(\\implies\\) x = \\(3\\pi\\over 2\\) for which tanx + secx = 2cosx\u00a0 is not defined.<\/p>\n

Thus, sinx = \\(1\\over 2\\) \\(\\implies\\) x = \\(\\pi\\over 6\\),\u00a0 \\(5\\pi\\over 6\\)<\/p>\n

\\(\\implies\\)\u00a0 number of solutions of tanx + secx = 2cosx is 2.<\/p>\n

\n

Similar Questions<\/h3>\n

If \\({1\\over 6}sin\\theta\\), \\(cos\\theta\\) and \\(tan\\theta\\) are in G.P. then the general solution for \\(\\theta\\) is<\/a><\/p>\n

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

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Find general solution of (2sinx \u2013 cosx)(1 + cosx) = \\(sin^2x\\)<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : Here, tanx + secx = 2cosx\u00a0 \u00a0 \u00a0 \u00a0\\(\\implies\\)\u00a0 \u00a0 \u00a0sinx + 1 = \\(2cos^2x\\) \\(\\implies\\) \\(2sin^2x\\) + sinx – 1 = 0\u00a0 \u00a0 \u00a0\\(\\implies\\)\u00a0 \u00a0 sinx = \\(1\\over 2\\), -1 But sinx = -1 \\(\\implies\\) x = \\(3\\pi\\over 2\\) for which tanx + secx = 2cosx\u00a0 is not defined. Thus, sinx = …<\/p>\n

Find the number of solutions of tanx + secx = 2cosx in [0, \\(2\\pi\\)].<\/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":"\nFind the number of solutions of tanx + secx = 2cosx in [0, \\(2\\pi\\)].<\/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-number-of-solutions-of-tanx-secx-2cosx-in-0-2pi\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Find the number of solutions of tanx + secx = 2cosx in [0, \\(2\\pi\\)].\" \/>\n<meta property=\"og:description\" content=\"Solution : Here, tanx + secx = 2cosx\u00a0 \u00a0 \u00a0 \u00a0(implies)\u00a0 \u00a0 \u00a0sinx + 1 = (2cos^2x) (implies) (2sin^2x) + sinx – 1 = 0\u00a0 \u00a0 \u00a0(implies)\u00a0 \u00a0 sinx = (1over 2), -1 But sinx = -1 (implies) x = (3piover 2) for which tanx + secx = 2cosx\u00a0 is not defined. 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