We're having trouble proving this trig identity:
$e^{i \alpha} + e^{i \beta} = 2e^{\frac{i(\alpha + \beta)}{2}}\cos(\frac{\alpha-\beta}{2})$
We've tried various manipulations using basic trig identities (too lengthy to show here) and come up with nasty equations that don't lead anywhere.
Can you point us in the right direction?