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CBSE Class 12-science Answered

If y = etan x  , prove that  (cos2 x)d2y/dx2 – ( 1 + sin 2x).dy/dx = 0 Explain in great detail
Asked by haroonrashidgkp | 25 Aug, 2018, 07:05: PM
Expert Answer
begin mathsize 16px style straight y equals straight e to the power of tanx dy over dx equals straight e to the power of tanx cross times sec squared straight x dy over dx equals ysec squared straight x......... left parenthesis straight i right parenthesis fraction numerator straight d squared straight y over denominator dx squared end fraction equals 2 ysecxsecxtanx plus sec squared straight x dy over dx fraction numerator straight d squared straight y over denominator dx squared end fraction equals 2 ysec squared xtanx plus sec squared straight x dy over dx cos squared straight x fraction numerator straight d squared straight y over denominator dx squared end fraction equals 2 ytanx plus dy over dx Consider comma LHS space equals space cos squared straight x fraction numerator straight d squared straight y over denominator dx squared end fraction minus left parenthesis 1 plus sin 2 straight x right parenthesis dy over dx equals 2 ytanx plus dy over dx minus dy over dx minus sin 2 straight x dy over dx equals 2 ytanx minus sin 2 straight x dy over dx equals 2 ytanx minus sin 2 straight x cross times ysec squared straight x....... from space left parenthesis straight i right parenthesis equals 2 straight y cross times sinx over cosx minus 2 ysinxcosx cross times fraction numerator 1 over denominator cos squared straight x end fraction equals 2 straight y cross times sinx over cosx minus 2 straight y cross times sinx over cosx equals 0 end style
Answered by Sneha shidid | 28 Aug, 2018, 10:54: AM

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