Originally Posted by
Mathstud28 $\displaystyle \cos^{2m}(x)$ or
$\displaystyle \sin^{2m}(x)$
where $\displaystyle m\in\mathbb{N}$
$\displaystyle \sin^{2m+1}(x)$
or $\displaystyle \cos^{2m+1}(x)$
$\displaystyle m\in\mathbb{Z^{+}}$
use pythagorean identity
$\displaystyle \sin\bigg(\frac{x}{2}\bigg)$
or $\displaystyle \cos\bigg(\frac{x}{2}\bigg)$
use half-angle formulas
$\displaystyle \cos(2mx)$
or $\displaystyle \sin(2mx)$
and $\displaystyle m\in\mathbb{N}$
use double angle formuals
NOTE the restrictions on m arent neccasary, but if m does not satisfy those conditions it is tricker because you get into radicals and such