# Prove identity involving powers and trigonometric functions

Need help proving that: $$(1+\cos\alpha+i\sin\alpha)^{n}= 2^{n}\cos^{n}\frac{\alpha}{2}\left(\cos\frac{n\alpha}{2}+i\sin\frac{n\alpha}{2}\right)$$

-
Hint: $\mathrm e^{\mathrm i\phi}=\cos\phi + \mathrm i\sin\phi$ –  celtschk Sep 30 '12 at 14:17
Hint: $$1 + \cos\alpha = 2\cos^2\frac{\alpha}{2} \\ \sin\alpha = 2\sin\frac{\alpha}{2}\cos\frac{\alpha}{2}$$