Consider: $\lim \limits \_{x\rightarrow 0} \frac{\pi(1-cos^mx)}{x^n}$.

The question is to find the value of $m$ and $n$ such that the limit above should exist. If one applies L'Hospitals rule, it is ending nowhere.
I want to use $1-\cos x=2\sin^2 \frac x 2$ or $1-\cos^2x=\sin^2x$,but as it is $1-\cos^mx$ nothing could be done. Can anyone help?