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Question

Find dydx, when
x=a(1cosθ) and y=a(θ+sinθ) at θ=π2

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Solution

We have,

x=a(1cosθ), y=a(θ+sinθ)

Differentiating w.r.t. θ, we get,

dxdθ=asinθ,dydθ=a(1+cosθ)

dydx=dy/dθdx/dθ=a(1+cosθ)asinθ=2cos2θ22sinθ2cosθ2=cotθ2

(dydx)θ=π2=cotπ4=1.

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