I've been self-studying some complex variables and just started on residues. I'm looking at a problem where I've been asked to calculate the residue of:
$f(z) = \frac{z}{1-\cos(z)}$
at $z=0$. I'm not really sure how to find the Laurent series of this function, and I can't really apply Cauchy's integral formula either. So I would appreciate if anyone can get me started.