{"id":9458,"date":"2022-01-14T15:29:11","date_gmt":"2022-01-14T09:59:11","guid":{"rendered":"https:\/\/mathemerize.com\/?p=9458"},"modified":"2022-01-14T16:24:17","modified_gmt":"2022-01-14T10:54:17","slug":"what-is-the-general-solution-of-sin2-theta-sin2-alpha","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/what-is-the-general-solution-of-sin2-theta-sin2-alpha\/","title":{"rendered":"What is the General Solution of \\(sin^2 \\theta\\) =\\(sin^2 \\alpha\\) ?"},"content":{"rendered":"

Solution :<\/h2>\n

The general solution of \\(sin^2 \\theta\\) = \\(sin^2 \\alpha\\)<\/strong> is given by \\(\\theta\\) = \\(n\\pi \\pm \\alpha\\), n \\(\\in\\) Z.<\/strong><\/p>\n

Proof :<\/strong><\/p>\n

We have, \\(sin^2 \\theta\\) =\\(sin^2 \\alpha\\)<\/p>\n

\\(\\implies\\)  \\(2 sin^2 \\theta\\) =\\(2 sin^2 \\alpha\\)<\/p>\n

\\(\\implies\\)  \\(1 – cos 2\\theta\\) = \\(1 – cos 2\\alpha\\)<\/p>\n

\\(\\implies\\)   \\(cos 2\\theta\\) = \\(cos 2\\alpha\\)<\/p>\n

\\(\\implies\\)  \\(2\\theta\\) = \\(2n\\pi \\pm 2\\alpha\\),  n \\(\\in\\)  Z.<\/p>\n

\\(\\implies\\)  \\(\\theta\\) = \\(n\\pi \\pm \\alpha\\), n \\(\\in\\) Z.<\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : The general solution of \\(sin^2 \\theta\\) = \\(sin^2 \\alpha\\) is given by \\(\\theta\\) = \\(n\\pi \\pm \\alpha\\), n \\(\\in\\) Z. Proof : We have, \\(sin^2 \\theta\\) =\\(sin^2 \\alpha\\) \\(\\implies\\)  \\(2 sin^2 \\theta\\) =\\(2 sin^2 \\alpha\\) \\(\\implies\\)  \\(1 – cos 2\\theta\\) = \\(1 – cos 2\\alpha\\) \\(\\implies\\)   \\(cos 2\\theta\\) = \\(cos 2\\alpha\\) \\(\\implies\\)  \\(2\\theta\\) …<\/p>\n

What is the General Solution of \\(sin^2 \\theta\\) =\\(sin^2 \\alpha\\) ?<\/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":"","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":"\nWhat is the General Solution of \\(sin^2 \\theta\\) =\\(sin^2 \\alpha\\) ?<\/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\/what-is-the-general-solution-of-sin2-theta-sin2-alpha\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"What is the General Solution of \\(sin^2 \\theta\\) =\\(sin^2 \\alpha\\) ?\" \/>\n<meta property=\"og:description\" content=\"Solution : The general solution of (sin^2 theta) = (sin^2 alpha) is given by (theta) = (npi pm alpha), n (in) Z. Proof : We have, (sin^2 theta) =(sin^2 alpha) (implies)  (2 sin^2 theta) =(2 sin^2 alpha) (implies)  (1 – cos 2theta) = (1 – cos 2alpha) (implies)   (cos 2theta) = (cos 2alpha) (implies)  (2theta) … What is the General Solution of (sin^2 theta) =(sin^2 alpha) ? 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Proof : We have, (sin^2 theta) =(sin^2 alpha) (implies)  (2 sin^2 theta) =(2 sin^2 alpha) (implies)  (1 – cos 2theta) = (1 – cos 2alpha) (implies)   (cos 2theta) = (cos 2alpha) (implies)  (2theta) … What is the General Solution of (sin^2 theta) =(sin^2 alpha) ? 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