{"id":9213,"date":"2022-01-03T16:23:55","date_gmt":"2022-01-03T10:53:55","guid":{"rendered":"https:\/\/mathemerize.com\/?p=9213"},"modified":"2022-01-03T19:11:14","modified_gmt":"2022-01-03T13:41:14","slug":"what-is-the-formula-of-sina-b","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/what-is-the-formula-of-sina-b\/","title":{"rendered":"What is the Formula of Sin(A + B) ?"},"content":{"rendered":"

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

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

The formula of sin(A + B)<\/strong> is sin A cos B + cos 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 sin (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

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

= \\(3\\over 5\\) \\(\\times\\) \\(9\\over 41\\) + \\(4\\over 5\\) \\(\\times\\) \\(40\\over 41\\) = \\(187\\over 205\\)<\/p>\n

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

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

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

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

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

\\(\\implies\\) sin 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 sin (A + B) with examples. Sin (A + B) Formula : The formula of sin(A + B) is sin A cos B + cos 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 Sin(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 Sin(A + B) ? - Mathemerize<\/title>\n<meta name=\"description\" content=\"In this post you will learn what is the formula of sin (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-sina-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 Sin(A + B) ? 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