Let the contour $\gamma$ be a positively oriented cifrcle of radius 2 centered at zero, traversed once.
Evaluate I = $\int_{\gamma}$ $\frac{dz}{(1-e^{iz})cosh(z)}$.
This is what Ive done so far
let $z = 2e^{i\theta}$ for 0 < $\theta$ < 2$\pi$
$dz$ = $2ie^{i\theta}$$d\theta$
So I = $\int_0^{2\pi}$ $\frac{2ie^{i\theta}d\theta}{(1-e^{2ie^{i\theta}}))cosh(2e^{i\theta})}$.
Is this the best way to do this question and where do i go from here?
Edit Just realised I can probably incorporate cosh($z$) = ($e^z$ + $e^{-z}$)/2