Thread: Partial fraction decomposition of tangent function

Hey, howdy!

My book asked me to show, using the relation cot(z/2) -tan(z/2) = 2 cot(z), that pi*tan(pi*z) = sum[(8*z)/((2*n+1)^2 - 4*z^2)]

But I was only able to get that pi*tan(pi*z) = sum[(2*z)/(z^2 - n^2) - (8*z)/(4*z^2 - n^2)].

Oh and I used, of course, that pi*cot(pi*z) = 1/z + sum[(2*z)/(z^2-n^2)].

How do I proceed from here?

Thanks!