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Question

If x=acos3θ,y=asin3θ, then 1+(dydx)2 is _____

A
tanθ
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B
tan2θ
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C
sec2θ
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D
1
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Solution

The correct option is D sec2θ
We have, x=acos3θ and y=asin3θ
Differentiate both w.r.t. θ
We get: dxdθ=3acos2θsinθ and dydθ=3asin2θcosθ

Thus dydx=dydθdxdθ=3asin2θcosθ3acos2θsinθ=tanθ

Therefore 1+(dydx)2=1+tan2θ=sec2θ

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