{"id":8505,"date":"2021-11-22T20:42:45","date_gmt":"2021-11-22T15:12:45","guid":{"rendered":"https:\/\/mathemerize.com\/?p=8505"},"modified":"2021-11-22T21:37:41","modified_gmt":"2021-11-22T16:07:41","slug":"find-dyover-dx-where-x-acos-t-1over-2-log-tan2-tover-2-and-y-a-sin-t","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/find-dyover-dx-where-x-acos-t-1over-2-log-tan2-tover-2-and-y-a-sin-t\/","title":{"rendered":"Find \\(dy\\over dx\\) where x = a{cos t + \\({1\\over 2} log tan^2 {t\\over 2}\\)} and y = a sin t"},"content":{"rendered":"

Solution :<\/h2>\n

We have, x = a{cos t + \\({1\\over 2} log tan^2 {t\\over 2}\\)} and y = a sin t<\/p>\n

\\(\\implies\\) x = a{cos t + \\({1\\over 2} \\times 2 log tan{t\\over 2}\\)} and y = a sin t<\/p>\n

\\(\\implies\\) x = a{cos t + {\\(log tan{t\\over 2}\\)} and y = a sin t<\/p>\n

By using differentiation of parametric functions<\/a>,<\/p>\n

Differentiating with respect to t, we get<\/p>\n

\\(dx\\over dt\\) = a{-sin t + \\({1\\over tan t\/2}(sec^2{t\\over 2})\\times {1\\over 2}\\)} and \\(dy\\over dt\\) = a cost<\/p>\n

\\(dx\\over dt\\) = a{-sin t + \\(1\\over 2 sin (t\/2) cos (t\/2)\\)} and \\(dy\\over dt\\) = a cost<\/p>\n

\\(\\implies\\)\u00a0 \\(dx\\over dt\\) = a{-sin t + \\(1\\over sint \\)} and \\(dy\\over dt\\) = a cost<\/p>\n

\\(\\implies\\)\u00a0 \\(dx\\over dt\\) = a{\\(-sin^2t + 1\\over sint \\)} and \\(dy\\over dt\\) = a cost<\/p>\n

\\(dx\\over dt\\) = a{\\(cos^2t\\over sint \\)} and \\(dy\\over dt\\) = a cost<\/p>\n

\\(\\therefore\\)\u00a0 \u00a0\\(dy\\over dx\\) = \\(dy\/dt\\over dx\/dt\\) = \\(acost\\over {acos^2t\\over sint}\\)<\/p>\n

\\(dy\\over dx\\) = tan t<\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : We have, x = a{cos t + \\({1\\over 2} log tan^2 {t\\over 2}\\)} and y = a sin t \\(\\implies\\) x = a{cos t + \\({1\\over 2} \\times 2 log tan{t\\over 2}\\)} and y = a sin t \\(\\implies\\) x = a{cos t + {\\(log tan{t\\over 2}\\)} and y = a sin t …<\/p>\n

Find \\(dy\\over dx\\) where x = a{cos t + \\({1\\over 2} log tan^2 {t\\over 2}\\)} and y = a sin t<\/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":[65,43],"tags":[],"yoast_head":"\nFind \\(dy\\over dx\\) where x = a{cos t + \\({1\\over 2} log tan^2 {t\\over 2}\\)} and y = a sin t<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, 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