I need help integrating this:
$\oint_{|z-1|=1} \sec(z) \, dz $
From the context of my course, I assume that what I'm suppose to do is expand $\sec(z)$ centered at $z_0=1$ into a Laurent series then find the residue, then use the formula to solve it. But expanding sec(z) centered at 1 seems too tedious, so I'm wondering if there is a better way. Also, I can't see any terms in the expansion that will contain $\frac1z$ so is the answer to the problem $0$? or am I missing something.