1. ## Trig Integral Identity

Hi I'm doing a dynamics problem, To get it into the form wanted I've reduced the problem to showing that
$
\int_{0}^{\pi/2} cos^2 x sin^8 x dx = \frac{1}{9} \int_{0}^{\pi/2} cos^{10} x dx
$

Apologies, the above latex code renders fine on my machine but it looks like the forum doesn't support it

It's meant to say
\int_{0}^{\pi/2} \cos^2 x \sin^8 x dx = \frac{1}{9} \int_{0}^{\pi/2} \cos^{10} x dx

Is there any obvious quick way of doing this, or a hint would be nice, I've thought of integrating it by parts but I cant quite see a nice way of splitting it.

2. Use parts: $u=\cos(x)~\&~dv=\cos(x)\sin^8(x)$