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`

Answer 1

(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`