Derivative of `tan^(3)theta` with respect to `sec^(3)theta` at `theta= – InterviewSolution

InterviewSolution

1.	Derivative of `tan^(3)theta` with respect to `sec^(3)theta` at `theta=(pi)/(3)` isA. `(3)/(2)`B. `(sqrt(3))/(2)`C. `(1)/(2)`D. `-(sqrt(3))/(2)`
Answer» Given `y = tan ^(3) theta, x sec^(3) theta` Differentiate both x and y w.r.t. `theta` `(dy)/(d theta)= 3 tan^(2) theta sec^(2) theta`. `(dx)/(d theta)= 3 sec^(2) theta xx sec theta tan theta` `(dy)/(dx)=(dy)/(d theta)xx(d theta)/(d)` `=(3 tan^(2) theta xx sec^(2) theta)/( 3 sec^(2) theta xx sec theta tan theta)` `=(tan theta)/(sec theta)=( sin theta)/(cos theta)xxcos theta ` `sin theta` At `theta =(pi)/(3)` `(dy)/(dx)= sin ((pi)/(3))= (sqrt(3))/(2)` Hence, correct answer from the given alternatives is (b).

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