{"id":6889,"date":"2021-10-21T22:05:33","date_gmt":"2021-10-21T16:35:33","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6889"},"modified":"2021-10-25T09:56:46","modified_gmt":"2021-10-25T04:26:46","slug":"find-general-solution-of-2sinx-cosx1-cosx-sin2x","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/find-general-solution-of-2sinx-cosx1-cosx-sin2x\/","title":{"rendered":"Find general solution of (2sinx – cosx)(1 + cosx) = \\(sin^2x\\)"},"content":{"rendered":"

Solution :<\/h2>\n

(2sinx – cosx)(1 + cosx) – (1 – \\(cos^2x\\)) = 0<\/p>\n

\\(\\therefore\\) (1 + cosx)(2sinx – cosx – 1 + cosx) = 0<\/p>\n

\\(\\therefore\\)\u00a0 (1 + cosx)(2sinx – 1) = 0<\/p>\n

\\(\\implies\\) cosx = -1\u00a0 or\u00a0 sinx = \\(1\\over 2\\)<\/p>\n

\\(\\implies\\)\u00a0 cosx = -1 = cos\\(\\pi\\)\u00a0 \\(\\implies\\)\u00a0 x = 2n\\(\\pi\\) + \\(\\pi\\) = (2n+1)\\(\\pi\\), n \\(\\in\\) I<\/p>\n

or\u00a0 sinx = \\(1\\over 2\\) = sin\\(\\pi\\over 6\\)\u00a0 \\(\\implies\\)\u00a0 x = k\\(\\pi + (-1)^k{\\pi\\over 6}\\), k \\(\\in\\) I<\/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

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

Find the number of solutions of tanx + secx = 2cosx in [0, \\(2\\pi\\)].<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : (2sinx – cosx)(1 + cosx) – (1 – \\(cos^2x\\)) = 0 \\(\\therefore\\) (1 + cosx)(2sinx – cosx – 1 + cosx) = 0 \\(\\therefore\\)\u00a0 (1 + cosx)(2sinx – 1) = 0 \\(\\implies\\) cosx = -1\u00a0 or\u00a0 sinx = \\(1\\over 2\\) \\(\\implies\\)\u00a0 cosx = -1 = cos\\(\\pi\\)\u00a0 \\(\\implies\\)\u00a0 x = 2n\\(\\pi\\) + \\(\\pi\\) = …<\/p>\n

Find general solution of (2sinx – cosx)(1 + cosx) = \\(sin^2x\\)<\/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 general solution of (2sinx - cosx)(1 + cosx) = \\(sin^2x\\)<\/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-general-solution-of-2sinx-cosx1-cosx-sin2x\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Find general solution of (2sinx - 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