{"id":9455,"date":"2022-01-14T16:23:09","date_gmt":"2022-01-14T10:53:09","guid":{"rendered":"https:\/\/mathemerize.com\/?p=9455"},"modified":"2022-01-14T16:23:11","modified_gmt":"2022-01-14T10:53:11","slug":"what-is-the-general-solution-of-tan-theta-tan-alpha","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/what-is-the-general-solution-of-tan-theta-tan-alpha\/","title":{"rendered":"What is the General Solution of \\(tan \\theta\\) = \\(tan \\alpha\\) ?"},"content":{"rendered":"

Solution :<\/h2>\n

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

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

We have, \\(tan \\theta\\) = \\(tan \\alpha\\)<\/p>\n

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

\\(\\implies\\)  \\(sin \\theta cos \\alpha\\) – \\(cos \\theta sin \\alpha\\) = 0<\/p>\n

\\(\\implies\\)  \\(sin (\\theta – \\alpha)\\) = 0<\/p>\n

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

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

Remark : <\/strong>Since \\(tan \\theta\\) = \\(tan \\alpha\\) is equivalent to \\(cot \\theta\\) = \\(cot \\alpha\\). So, general solutions of \\(cot \\theta\\) = \\(cot \\alpha\\) and \\(tan \\theta\\) = \\(tan \\alpha\\) are same.<\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : The general solution of \\(tan \\theta\\) = \\(tan \\alpha\\) is given by \\(\\theta\\) = \\(n\\pi + \\alpha\\),  n \\(\\in\\) Z. Proof : We have, \\(tan \\theta\\) = \\(tan \\alpha\\) \\(\\implies\\)  \\(sin \\theta\\over cos \\theta\\) = \\(sin \\alpha\\over cos \\alpha\\) \\(\\implies\\)  \\(sin \\theta cos \\alpha\\) – \\(cos \\theta sin \\alpha\\) = 0 \\(\\implies\\)  \\(sin …<\/p>\n

What is the General Solution of \\(tan \\theta\\) = \\(tan \\alpha\\) ?<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","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 \\(tan \\theta\\) = \\(tan \\alpha\\) ? - Mathemerize<\/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-tan-theta-tan-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 \\(tan \\theta\\) = \\(tan \\alpha\\) ? - Mathemerize\" \/>\n<meta property=\"og:description\" content=\"Solution : The general solution of (tan theta) = (tan alpha) is given by (theta) = (npi + alpha),  n (in) Z. 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