{"id":9185,"date":"2022-01-01T00:14:29","date_gmt":"2021-12-31T18:44:29","guid":{"rendered":"https:\/\/mathemerize.com\/?p=9185"},"modified":"2022-01-01T00:41:22","modified_gmt":"2021-12-31T19:11:22","slug":"prove-that-cosec90-theta-sectheta","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/prove-that-cosec90-theta-sectheta\/","title":{"rendered":"Prove that \\(Cosec(90 – \\theta)\\) = \\(Sec\\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

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

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

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

\\(cosec(90 – \\theta)\\) = \\(sec\\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\\) sec A = \\(sec\\theta\\) = \\(AC\\over AB\\)                     ……..(1) cosec C = \\(cosec(90 – \\theta)\\) = \\(AC\\over AB\\)            …<\/p>\n

Prove that \\(Cosec(90 – \\theta)\\) = \\(Sec\\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 \\(Cosec(90 - \\theta)\\) = \\(Sec\\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-cosec90-theta-sectheta\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Prove that \\(Cosec(90 - \\theta)\\) = \\(Sec\\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) sec A = (sectheta) = (ACover AB)                     ……..(1) cosec C = (cosec(90 – theta)) = (ACover AB)            … Prove that (Cosec(90 – theta)) = (Sectheta). 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