if y = (1- sin2x/1 + sin 2x)1/2 show that dy/dx + sec2(π/4 – x) = 0

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Asked by haroonrashidgkp | 11th Jul, 2018, 12:32: PM

Expert Answer:

begin mathsize 16px style straight y equals square root of fraction numerator 1 minus sin 2 straight x over denominator 1 plus sin 2 straight x end fraction end root
straight y equals square root of fraction numerator left parenthesis cosx minus sinx right parenthesis squared over denominator open parentheses cosx plus sinx close parentheses squared end fraction end root
straight y equals fraction numerator cosx minus sinx over denominator cosx plus sinx end fraction
dy over dx equals fraction numerator open parentheses cosx plus sinx close parentheses open parentheses negative sinx minus cosx close parentheses minus left parenthesis cosx minus sinx right parenthesis left parenthesis negative sinx plus cosx right parenthesis over denominator left parenthesis cosx plus sinx right parenthesis squared end fraction
dy over dx equals fraction numerator negative open parentheses cosx plus sinx close parentheses squared minus open parentheses cosx minus sinx close parentheses squared over denominator left parenthesis cosx plus sinx right parenthesis squared end fraction
dy over dx equals fraction numerator negative open parentheses cos squared straight x plus sin squared straight x plus 2 sinxcosx close parentheses minus open parentheses cos squared straight x plus sin squared straight x minus 2 sinxcosx close parentheses over denominator left parenthesis cosx plus sinx right parenthesis squared end fraction
dy over dx equals fraction numerator negative 1 minus 2 sinxcosx minus 1 plus 2 sinxcosx over denominator left parenthesis cosx plus sinx right parenthesis squared end fraction
dy over dx equals fraction numerator negative 2 over denominator left parenthesis cosx plus sinx right parenthesis squared end fraction
If space you space solve space sec squared open parentheses straight pi over 4 minus straight x over 2 close parentheses space you space get space sec squared open parentheses straight pi over 4 minus straight x over 2 close parentheses equals fraction numerator 2 over denominator left parenthesis cosx plus sinx right parenthesis squared end fraction
dy over dx equals fraction numerator negative 2 over denominator left parenthesis cosx plus sinx right parenthesis squared end fraction equals negative space sec squared open parentheses straight pi over 4 minus straight x over 2 close parentheses
dy over dx plus sec squared open parentheses straight pi over 4 minus straight x over 2 close parentheses equals 0
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Answered by Sneha shidid | 11th Jul, 2018, 03:03: PM