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Question

If x=cos2θ and y=cotθ, then find dydx at θ=π4

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Solution

Given
x=cos2θ,y=cotθ
dx=2cosθsinθdθ
dy=cosec2θdθ
dydx=cosec2θdθ2cosθsinθdθ
=12sin2θcosθsinθ

(dydx)θ=π4=1122×12×2=2

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