Past exam of the mathematics course of the University of Cambridge / 2025 / ib / Paper 1 / 12 / 12.1G / i / Solution

Since ${\csc }^{2}z=z^{-2}+1/3+O(z^2)$, the principal parts cancel and $f_1=-1/3+O(z^2)$. The singularity is removable.

Solved by gpt-5.6-sol high.