{"id":9325,"date":"2022-01-10T00:13:01","date_gmt":"2022-01-09T18:43:01","guid":{"rendered":"https:\/\/mathemerize.com\/?p=9325"},"modified":"2022-01-16T17:13:36","modified_gmt":"2022-01-16T11:43:36","slug":"what-is-the-formula-of-tan-2a","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/what-is-the-formula-of-tan-2a\/","title":{"rendered":"Tan 2A Formula – Proof and Examples"},"content":{"rendered":"

Here you will learn what is the formula of tan 2A in terms of tan with proof and examples based on it.<\/p>\n

Let’s begin –<\/p>\n

Tan 2A Formula :<\/h2>\n
\n

The formula of tan 2A is \\(2 tan A\\over 1 – tan^2 A\\)<\/p>\n<\/blockquote>\n

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

We have,<\/p>\n

tan (A + B) = \\(tan A + tan B\\over 1 – tan A tan B\\)<\/p>\n

Replacing B by A,<\/p>\n

\\(\\implies\\)  tan 2A = \\(tan A + tan A\\over 1 – tan A tan A\\)<\/p>\n

\\(\\implies\\)  tan 2A = \\(2 tan A\\over 1 – tan^2 A\\)<\/p>\n

We can also write above relation in terms of angle A\/2, just replace A by A\/2, we get<\/p>\n

\n

tan 2A = \\(2 tan ({A\\over 2})\\over 1 – tan^2 ({A\\over 2})\\)<\/p>\n<\/blockquote>\n

Example<\/strong><\/span> : Find the value of Tan 120 Degrees ?<\/p>\n

Solution<\/span><\/strong> : We Know that tan 60 = \\(\\sqrt{3}\\).<\/p>\n

By using above formula, tan 2A = \\(2 tan A\\over 1 – tan^2 A\\)<\/p>\n

tan 120 = \\(2 tan 60\\over 1 – tan^2 60\\) = \\(2 \\times \\sqrt{3}\\over 1 – 3\\)<\/p>\n

\\(\\implies\\)  tan 120 = \\(-\\sqrt{3}\\)<\/p>\n

Example<\/strong><\/span> : If sin A = \\(3\\over 5\\), where 0 < A < 90 degrees, find the value of tan 2A ?<\/p>\n

Solution<\/span><\/strong> : We have,<\/p>\n

sin A = \\(3\\over 5\\) where 0 < A < 90 degrees<\/p>\n

\\(\\therefore\\) \\(cos^2 A\\) = 1 – \\(sin^2 A\\)<\/p>\n

\\(\\implies\\) cos A = \\(\\sqrt{1 – sin^2 A}\\) = \\(\\sqrt{1 – {9\\over 25}}\\) = \\(4\\over 5\\)<\/p>\n

\\(\\implies\\) tan A = \\(sin A\\over cos A\\) = \\(3\/5\\over 4\/5\\) = \\(3\\over 4\\)<\/p>\n

By using above formula,<\/p>\n

tan 2A = \\(2 tan A\\over 1 – tan^2 A\\) = \\(2 \\times {3\\over 4} \\over 1 – {9\\over 16}\\)<\/p>\n

\\(\\implies\\) tan 2A = \\({6\\over 4}\\over {7\\over 16}\\)<\/p>\n

\\(\\implies\\)  tan 2A = \\(24\\over 7\\)<\/p>\n\n\n

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

Here you will learn what is the formula of tan 2A in terms of tan with proof and examples based on it. Let’s begin – Tan 2A Formula : The formula of tan 2A is \\(2 tan A\\over 1 – tan^2 A\\) Proof : We have, tan (A + B) = \\(tan A + tan …<\/p>\n

Tan 2A Formula – Proof and Examples<\/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":[28],"tags":[728,727],"yoast_head":"\nTan 2A Formula - Proof and Examples - Mathemerize<\/title>\n<meta name=\"description\" content=\"In this post you will learn what is the formula of tan 2A in terms of tan with proof and examples based on it.\" \/>\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-formula-of-tan-2a\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Tan 2A Formula - 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