If y = (cosec x + cot x ), prove that (sinx)d2y/dx2 – y2 = 0

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Asked by haroonrashidgkp | 24th Aug, 2018, 11:11: PM

Expert Answer:

begin mathsize 16px style straight y equals cosecx plus cotx
dy over dx equals negative cosecxcotx minus cosec squared straight x
dy over dx equals fraction numerator negative cotx over denominator sinx end fraction minus cosecx over sinx
dy over dx equals fraction numerator negative 1 over denominator sinx end fraction straight y
sinx dy over dx equals negative straight y............. left parenthesis straight i right parenthesis
sinx fraction numerator straight d squared straight y over denominator dx squared end fraction plus dy over dx cosx equals negative dy over dx
sinx fraction numerator straight d squared straight y over denominator dx squared end fraction equals negative dy over dx cosx minus dy over dx
sinx fraction numerator straight d squared straight y over denominator dx squared end fraction equals negative open parentheses 1 plus cosx close parentheses fraction numerator negative straight y over denominator sinx end fraction............. from space left parenthesis straight i right parenthesis
sinx fraction numerator straight d squared straight y over denominator dx squared end fraction equals fraction numerator open parentheses 1 plus cosx close parentheses over denominator sinx end fraction straight y
sinx fraction numerator straight d squared straight y over denominator dx squared end fraction equals open parentheses cosecx plus cotx close parentheses straight y
sinx fraction numerator straight d squared straight y over denominator dx squared end fraction equals straight y squared
sinx fraction numerator straight d squared straight y over denominator dx squared end fraction minus straight y squared equals 0 end style

Answered by Sneha shidid | 27th Aug, 2018, 10:40: AM