How Do You Find the Laurent Expansion of sin(z)/(z-1) at z=1?

[Je m'appelle]

Homework Statement

I'm supposed to find the Laurent expansion of sin z/(z-1) at z=1.

The Attempt at a Solution

I thought about expanding the sine as a power series of (z-1) but I'm not so sure if that would be correct since the sine is a function of z and not z-1.

 

[andrien]

put z=1+h,
then sin(1+h)/h.now you can expand it