Have come across a limits questions I am having trouble with.

(1) $\displaystyle \lim_{x\to \pi}~\frac{\pi-x}{\sin{x}}$

$\displaystyle = \lim_{x\to \pi}~\left(\frac{\pi}{\sin{x}} - \frac{x}{\sin{x}}\right)$

I get stuck after that...I know that $\displaystyle \lim_{x\to 0}~\frac{\sin{x}}{x} = 1 ~$but not sure what to do when the limit is for $\displaystyle \pi$, and also the first part becomes undefined which is not the answer - the limit exists. Any tips?

EDIT: sorry I just realised that $\displaystyle \sin{x} = \sin{(\pi-x)}$ and now it is simple - so Q solved!