# Prove identity involving powers and trigonometric functions

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

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

## 1 Answer

Hint: $$1 + \cos\alpha = 2\cos^2\frac{\alpha}{2} \\ \sin\alpha = 2\sin\frac{\alpha}{2}\cos\frac{\alpha}{2}$$

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Thankyou @Ayman Hourieh. –  Mykolas Sep 30 '12 at 14:23
@Mykolas You're welcome! –  Ayman Hourieh Sep 30 '12 at 14:42