Hi, the question is: starting from the definition of the complex cosine function, prove the trig identity:

$\displaystyle cos^2z=\frac{1}{2}(1 + cos 2z)$

here's what i got

$\displaystyle cos^2 z = [\frac{1}{2}(e^{iz}+e^{-iz}]^2 $

$\displaystyle = \frac{1}{4}(e^{2iz}+e^{-2iz} + 2) $

$\displaystyle = \frac{1}{2}(\frac{1}{2} (e^{2iz} + e^{-2iz} + 1) $

and now i don't know what to do.. is this right so far? and can someone please help me finish it off?