{"id":9222,"date":"2022-01-03T17:46:54","date_gmt":"2022-01-03T12:16:54","guid":{"rendered":"https:\/\/mathemerize.com\/?p=9222"},"modified":"2022-01-03T19:12:52","modified_gmt":"2022-01-03T13:42:52","slug":"what-is-the-formula-of-cosa-b","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/what-is-the-formula-of-cosa-b\/","title":{"rendered":"What is the Formula of Cos(A + B) ?"},"content":{"rendered":"

In this post you will learn what is the formula for cos (A + B) with examples.<\/p>\n

Cos (A + B) Formula :<\/h2>\n

The formula of cos(A + B)<\/strong> is cos A cos B – sin A sin B<\/strong>.<\/p><\/blockquote>\n

Example<\/span><\/strong> : If sin A = \\(3\\over 5\\) and cos B = \\(9\\over 41\\), find the value of cos (A + B).<\/p>\n

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

sin A = \\(3\\over 5\\) and cos B = \\(9\\over 41\\)<\/p>\n

\\(\\therefore\\)  cos A = \\(\\sqrt{1 – sin^2 A}\\)  and  sin B = \\(\\sqrt{1 – cos^2 B}\\)<\/p>\n

\\(\\implies\\)  cos A = \\(\\sqrt{1 – {9\\over 25}}\\) = \\(4\\over 5\\)  and  sin B = \\(\\sqrt{1 – {81\\over 1681}}\\) = \\(40\\over 41\\)<\/p>\n

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

cos (A + B) = cos A cos B – sin A sin B<\/p>\n

= \\(4\\over 5\\) \\(\\times\\) \\(9\\over 41\\) – \\(3\\over 5\\) \\(\\times\\) \\(40\\over 41\\) = \\(-84\\over 205\\)<\/p>\n

Example<\/span><\/strong> : Find the value of cos 75.<\/p>\n

Solution<\/span><\/strong> : cos 75 = cos (45 + 30)<\/p>\n

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

cos (45 + 30) = cos 45 cos 30 – sin 45 sin 30<\/p>\n

\\(\\implies\\) cos 75 = \\(1\\over \\sqrt{2}\\) \\(\\times\\) \\(\\sqrt{3}\\over 2\\) – \\(1\\over \\sqrt{2}\\) \\(\\times\\) \\(1\\over 2\\)<\/p>\n

\\(\\implies\\) cos 75 = \\(\\sqrt{3} – 1\\over 2\\sqrt{2}\\)<\/p>\n","protected":false},"excerpt":{"rendered":"

In this post you will learn what is the formula for cos (A + B) with examples. Cos (A + B) Formula : The formula of cos(A + B) is cos A cos B – sin A sin B. Example : If sin A = \\(3\\over 5\\) and cos B = \\(9\\over 41\\), find the …<\/p>\n

What is the Formula of Cos(A + B) ?<\/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":[],"yoast_head":"\nWhat is the Formula of Cos(A + B) ? - Mathemerize<\/title>\n<meta name=\"description\" content=\"In this post you will learn what is the formula of cos (A + B) with 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-cosa-b\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"What is the Formula of Cos(A + B) ? 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