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Question

If cos y=xcos(a+y) then prove that:
dydx=cos2(a+y)sina

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Solution

Given,

cosy=xcos(a+y)

x=cosycos(a+y)

differentiating w.r.t x, we get,

ddx(x)=ddx(cosycos(a+y))

1=ddy(cosycos(a+y))×dydx

1=(sin(a+y)cosycos(a+y)sinycos2(a+y))×dydx

1=(sin((a+y)y)cos2(a+y))×dydx

1=sinacos2(a+y)dydx

dydx=cos2(a+y)sina

Hence proved.

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