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CBSE Class 12-science Answered

if x=a(1-cosθ ),y =b sinθ , then find dy/dx and d^2y/dx^2.
Asked by Gothai | 28 Aug, 2018, 11:33: PM
answered-by-expert Expert Answer
begin mathsize 16px style straight x equals straight a left parenthesis 1 minus cosθ right parenthesis
dx over dθ equals asinθ........... left parenthesis straight i right parenthesis
straight y equals bsinθ
dy over dθ equals bcosθ....... left parenthesis ii right parenthesis
dy over dx equals fraction numerator begin display style dy over dθ end style over denominator dx over dθ end fraction
dy over dx equals fraction numerator begin display style bcosθ end style over denominator asinθ end fraction
dy over dx equals straight b over straight a cotθ
fraction numerator straight d squared straight y over denominator dx squared end fraction equals straight b over straight a cosec squared straight theta cross times dθ over dx
fraction numerator straight d squared straight y over denominator dx squared end fraction equals straight b over straight a cosec squared straight theta cross times fraction numerator 1 over denominator dx over dθ end fraction
fraction numerator straight d squared straight y over denominator dx squared end fraction equals straight b over straight a cosec squared straight theta cross times 1 over asinθ
fraction numerator straight d squared straight y over denominator dx squared end fraction equals straight b over straight a squared cosec cubed straight theta end style
Answered by Sneha shidid | 29 Aug, 2018, 09:31: AM
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