I am having problem with this question. Near $z = a + k\pi$ I found the principal part and it was $\frac{a}{z-a-kpi}$, but I saw on Wolframalpha that the answer is $\frac{\sin(a)}{z-a-kpi}$. I am using a tablet so it is difficult to write here what I did, but I did it in the usual way, expandind the functions near this point and then manipulating the denominator to find the principal part. I used the substitution $t = z - a - k\pi$ then I had to expand the function $\frac{\sin(t+a)}{\sin t}$. Can anyone help me? Thanks.
2026-03-27 19:55:06.1774641306
Find the principal part of $\frac{\sin z}{\sin(z-a)}$
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