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Question

If xcos(a+y)=cosy, then prove that dydx=cos2(a+y)sina. Show that sinad2ydx2+sin2(a+y)dydx=0.

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Solution

    xcos(a+y)=cosy,

    Which implies x=cosycos(a+y),
    Now differentiate on both sides , we get
      dx=cos(a+y)(siny)cosy(sin(a+y))cos2(a+y)dy=sin(a+yy)cos2(a+y)dy=sinacos2(a+y)dy

        dydx=cos2(a+y)sina

          d2ydx2=2cos(a+y)(sin(a+y)sina×dydx=sin2(a+y)sina×dydx

            Therefore, sinad2ydx2+sin2(a+y)dydx=0

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