Standard Wallis-type reduction for sine powers for JEE

Formula

\[I_n=\int_0^{\pi/2}\sin^n x\,dx=\frac{n-1}{n}I_{n-2}\]

Variables: \(n\ge 2\); \(I_n\) denotes the integral.

Conditions: Similarly valid for \(\cos^n x\). Bases: \(I_0=\frac{\pi}{2},\ I_1=1\).

Evaluation of trigonometric power definite integrals.