{"id":9175,"date":"2021-12-31T23:59:51","date_gmt":"2021-12-31T18:29:51","guid":{"rendered":"https:\/\/mathemerize.com\/?p=9175"},"modified":"2022-01-01T00:32:15","modified_gmt":"2021-12-31T19:02:15","slug":"prove-that-sin90-theta-costheta","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/prove-that-sin90-theta-costheta\/","title":{"rendered":"Prove that \\(Sin(90 – \\theta)\\) = \\(Cos\\theta\\)."},"content":{"rendered":"

Solution :<\/h2>\n

Draw a right angled triangle ABC right angled at B.\"theta\"<\/p>\n

Let \\(\\angle\\) A = \\(\\theta\\),  then \\(\\angle\\) C = 90 – \\(\\theta\\)<\/p>\n

cos A = \\(cos\\theta\\) = \\(AB\\over AC\\)                     ……..(1)<\/p>\n

sin C = \\(sin(90 – \\theta)\\) = \\(AB\\over AC\\)             ……..(2)<\/p>\n

From (1) and (2), we have<\/p>\n

\\(sin(90 – \\theta)\\) = \\(cos\\theta\\)<\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : Draw a right angled triangle ABC right angled at B. Let \\(\\angle\\) A = \\(\\theta\\),  then \\(\\angle\\) C = 90 – \\(\\theta\\) cos A = \\(cos\\theta\\) = \\(AB\\over AC\\)                     ……..(1) sin C = \\(sin(90 – \\theta)\\) = \\(AB\\over AC\\)            …<\/p>\n

Prove that \\(Sin(90 – \\theta)\\) = \\(Cos\\theta\\).<\/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(90 - \\theta)\\) = \\(Cos\\theta\\). - Mathemerize<\/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-sin90-theta-costheta\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Prove that \\(Sin(90 - \\theta)\\) = \\(Cos\\theta\\). - Mathemerize\" \/>\n<meta property=\"og:description\" content=\"Solution : Draw a right angled triangle ABC right angled at B. Let (angle) A = (theta),  then (angle) C = 90 – (theta) cos A = (costheta) = (ABover AC)                     ……..(1) sin C = (sin(90 – theta)) = (ABover AC)            … Prove that (Sin(90 – theta)) = (Costheta). 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