Problem 1561 (difficulty: 6/10)

Let \(\displaystyle D_\varepsilon\) be the domain that one gets by deleting discs with center \(\displaystyle k\pi\) (\(\displaystyle k\in\Z\)) and radius \(\displaystyle \varepsilon<\pi/2\). Show that both \(\displaystyle 1/\sin z\) and \(\displaystyle \ctg z\) are bounded on \(\displaystyle D_\varepsilon\).

Give me another random problem!