{"id":9258,"date":"2022-01-05T00:16:00","date_gmt":"2022-01-04T18:46:00","guid":{"rendered":"https:\/\/mathemerize.com\/?p=9258"},"modified":"2022-01-05T00:22:13","modified_gmt":"2022-01-04T18:52:13","slug":"prove-that-sin-a-b-sin-a-b-sin2-a-sin2-b","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/prove-that-sin-a-b-sin-a-b-sin2-a-sin2-b\/","title":{"rendered":"Prove that sin (A + B) sin (A – B) = \\(sin^2 A\\) – \\(sin^2 B\\)."},"content":{"rendered":"

Solution :<\/h2>\n

We have,<\/p>\n

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

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

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

= \\(sin^2 A\\) – \\(sin^2 A sin^2 B\\) – \\(sin^2 B\\) + \\(sin^2 A sin^2 B\\)<\/p>\n

= \\(sin^2 A – sin^2 B\\)<\/p>\n

Now, we can also write it as,<\/p>\n

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

Hence, sin (A + B) sin (A – B) = \\(sin^2 A\\) – \\(sin^2 B\\) = \\(cos^2 B\\) – \\(cos^2 A\\)<\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : We have, sin (A + B) sin (A – B) = (sin A cos B + cos A sin B) (sin A  cos B – cos A sin B) = \\(sin^2 A cos^2 B\\) – \\(cos^2 A sin^2 B\\) = \\(sin^2 A (1 – sin^2 B)\\) – \\((1 – sin^2 A) sin^2 B\\) …<\/p>\n

Prove that sin (A + B) sin (A – B) = \\(sin^2 A\\) – \\(sin^2 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":[43,60],"tags":[],"yoast_head":"\nProve that sin (A + B) sin (A - B) = \\(sin^2 A\\) - \\(sin^2 B\\).<\/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\/prove-that-sin-a-b-sin-a-b-sin2-a-sin2-b\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Prove that sin (A + B) sin (A - B) = \\(sin^2 A\\) - \\(sin^2 B\\).\" \/>\n<meta property=\"og:description\" content=\"Solution : We have, sin (A + B) sin (A – B) = (sin A cos B + cos A sin B) (sin A  cos B – cos A sin B) = (sin^2 A cos^2 B) – (cos^2 A sin^2 B) = (sin^2 A (1 – sin^2 B)) – ((1 – sin^2 A) sin^2 B) … Prove that sin (A + B) sin (A – B) = (sin^2 A) – (sin^2 B). 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