Find the singularities of $$\frac{1}{1-\cos{z}}$$
My attempt: $$1-\cos{z} = 0 \iff \cos{z} = 1 \iff z = 2k\pi, k \in Z$$and I would anser that the degree is 1, since we don't have $1-(\cos{z})^2$.
My textbook does indeed state that $z=2k\pi$ is the singularities, but that they have a degree of 2. Why?