- #1

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## Homework Statement

Prove that ## \sin(z_1+z_2) = \sin z_1\cos z_2+\sin z_2\cos z_1## such that ##z_1,z_2\in\mathbb{C}##

## Homework Equations

##\sin z = \sum\limits_{n=1, \mathrm{ odd}}^\infty (-1)^{(n-1)/2}\dfrac{z^n}{n!} = \sum\limits_{s=0}^\infty (-1)^s\dfrac{z^{2s+1}}{(2s+1)!}##

##\cos z = \sum\limits_{n=0, \mathrm{ even}}^\infty (-1)^{n/2}\dfrac{z^n}{n!} = \sum\limits_{s=0}^\infty (-1)^s\dfrac{z^{2s}}{(2s)!}##

## The Attempt at a Solution

I tried to just put ##\sin(z_1+z_2)## into de sin series but I get binomial of ##s##, don't think expanding it would do the trick. Maybe there's a subtle detail to solve this one.