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Question

If cosy=xcos(a+y), with cosa±1, prove that dydx=cos2(a+y)sina

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Solution

We have, cosy=xcos(a+y)(1)
Differentiate both sides w.r.t. x
sinydydx=cos(a+y)xsin(a+y)dydx
dydx=cos(a+y)xsin(a+y)siny=cos(a+y)cosycos(a+y)sin(a+y)siny
=cos2(a+y)cosysin(a+y)sinycos(a+y)=cos2(a+y)sina
Since sin(AB)=sinAcosBsinBcosA

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