Wallis formula for even powers for JEE

Formula

\[\int_0^{\pi/2}\sin^{2n}x\,dx=\int_0^{\pi/2}\cos^{2n}x\,dx=\frac{(2n-1)!!}{(2n)!!}\cdot\frac{\pi}{2}\]

Variables: \(n\in\mathbb{N}\); \((2n-1)!!=1\cdot 3\cdot 5\cdots(2n-1)\), \((2n)!!=2\cdot 4\cdot 6\cdots 2n\).

Standard definite values for even powers.