Starting from the default cosine recursion formal (top equation) how do you reach the bottom recursion formula which is for odd powers of cosine?
$$ \int \cos^n x \,dx = \frac1n\, \sin x \cos^{n-1}x + \frac{n-1}n \int \cos^{n-2}x \,dx $$
$$ I_{2n+1} = \int_0^{\pi/2} \cos^{2n+1}x \,dx = \frac{2\cdot 4\cdot 6\cdots(2n)}{3\cdot 5\cdot 7 \cdots(2n+1)}. $$
