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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

Given
cosy=xcos(a+y)
cosycos(a+y)=x
Diff w.r.t 'x'
d(x)dx=ddx(cosycos(a+y))
1=ddx(cosycos(a+y)).dydy
1=ddy(cosycos(a+y)).dydx
1=⎜ ⎜ ⎜ ⎜d(cosy)dy.cos(a+y)d(cos(a+y))dy.cosy(cos(a+y))2⎟ ⎟ ⎟ ⎟.dydx
1=⎜ ⎜ ⎜ ⎜siny.cos(a+y)(sin(a+y))d(a+y)dy.cosycos2(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
cos2(a+y)sin(a)=dydx

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