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Question

If x=a sec3 θ and y=a tan3 θ, then thevalue of dydx at θ=π3 is


A
12
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B
1
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C
32
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D
12
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Solution

The correct option is C 32
We have, x=a sec3 θ and y=a tan3 θDifferentiating w.r.t. θ, we getdxdθ=3a sec2 θ ddθ(sec θ)=3a sec3 θ tan θdydθ=3a tan2 θ ddθ(tan θ)=3a sec2 θ tan2 θdydx=dy/dθdx/dθ=3a sec2 θ tan2 θ3a sec3 θ tan θ=tan θsec θ=sin θ(dydx)θ=π3=sin π3=32

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