The formula of tan 3A<\/strong> is \\(3 tan A – tan^3 A\\over 1 – 3 tan^2 A\\).<\/strong><\/p><\/blockquote>\nProof :<\/strong><\/p>\nWe have,<\/p>\n
tan (A + B) = \\(tan A + tan B\\over 1 – tan A tan B\\)<\/p>\n
Replacing B by 2A,<\/p>\n
\\(\\implies\\) tan 3A = \\(tan A + tan 2A\\over 1 – tan A tan 2A\\)<\/p>\n
Since, tan 2A = \\(2 tan A\\over tan^2 A\\)<\/p>\n
\\(\\implies\\) tan 3A = \\(tan A + {2 tan A\\over tan^2 A}\\over 1 – tan A \\times {2 tan A\\over tan^2 A}\\)<\/p>\n
\\(\\implies\\) tan 3A = \\(tan A (1 – tan^2 A) + 2 tan A\\over 1 – tan^2 A – 2 tan^2 A\\) = \\(3 tan A – tan^3 A\\over 1 – 3 tan^2 A\\)<\/p>\n
Hence, tan 3A = \\(3 tan A – tan^3 A\\over 1 – 3 tan^2 A\\)<\/p>\n
We can also write above relation of angle A in terms of angle A\/3, just replace A by A\/3, we get<\/p>\n
tan A = \\(3 tan ({A\\over 3}) – tan^3 ({A\\over 3})\\over 1 – 3 tan^2 ({A\\over 3})\\)<\/p><\/blockquote>\n
Example<\/strong><\/span> : Prove that tan A + tan (60 + A) – tan (60 – A) = 3 tan 3A.<\/p>\nSolution<\/span><\/strong> : We have,<\/p>\nL.H.S = tan A + tan (60 + A) – tan (60 – A)<\/p>\n
\\(\\implies\\) L.H.S = tan A + \\(\\sqrt{3} + tan A\\over 1 – \\sqrt{3} tan A\\) – \\(\\sqrt{3} – tan A\\over 1 + \\sqrt{3} tan A\\)<\/p>\n
[ By using this formula, tan (A + B) = \\(tan A + tan B\\over 1 – tan A tan B\\) above ]<\/p>\n
\\(\\implies\\) L.H.S = tan A + \\(8 tan A\\over 1 – 3 tan^2 A\\)<\/p>\n
\\(\\implies\\) L.H.S = \\(9 tan A – 3 tan^3 A\\over 1 – 3 tan^2 A\\)<\/p>\n
L.H.S = 3(\\(3 tan A – tan^3 A\\over 1 – 3 tan^2 A\\))<\/p>\n
Since \\(3 tan A – tan^3 A\\over 1 – 3 tan^2 A\\) = tan 3A<\/p>\n
\\(\\implies\\) L.H.S = 3 tan 3A = R.H.S<\/p>\n","protected":false},"excerpt":{"rendered":"
Here you will learn what is the formula of tan 3A in terms of A with proof and examples based on it. Let’s begin – Tan 3A Formula The formula of tan 3A is \\(3 tan A – tan^3 A\\over 1 – 3 tan^2 A\\). Proof : We have, tan (A + B) = \\(tan …<\/p>\n
Tan 3A 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":[734,733],"yoast_head":"\nTan 3A Formula - Proof and Examples - Mathemerize<\/title>\n<meta name=\"description\" content=\"In this post you will learn what is the formula of tan 3A in terms of A 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\/tan-3a-formula-proof-examples\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Tan 3A Formula - 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