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## Homework Statement

Find the residues of the function

## Homework Equations

f(z)=[itex]\frac{1}{sin(z)}[/itex] at z=0, [itex]\frac{∏}{2}[/itex], ∏

## The Attempt at a Solution

Since the function has a simple pole at z=0

I used: Res(f,0)=lim[itex]_{z->0}[/itex](z-0)[itex]\cdot[/itex][itex]\frac{1}{sin(z)}[/itex]=1. This means the residue of the function at z=0 is 1.

And Res(f,[itex]\frac{∏}{2}[/itex])=lim[itex]_{z->∏/2}[/itex](z-[itex]\frac{∏}{2}[/itex])[itex]\cdot[/itex][itex]\frac{1}{sin(z)}[/itex]=0. This means the residue of the function at z=[itex]\frac{∏}{2}[/itex] is 0.

However I think this method can not be applied on solving z=∏. How can I work it out?

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