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Question
Derivatives of tan3θ with respect to sec3θ at θ=π/3 is
(A)` 3/2`
(B) `sqrt3/2`
(C) `1/2`
(D) `-sqrt3/2`
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Solution
(B) `sqrt3/2`
Let `y = tan^3theta , and x = sec^3theta`
`dy/(d theta)=3tan^2theta.sec^2theta, dx/(d theta)=3sec^2theta.secthetatantheta`
`dy/dx=sintheta=sin(pi/3)=sqrt3/2`
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