Prove identity involving powers and trigonometric functions

Question

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

Ayman Hourieh · Accepted Answer · 2012-09-30 14:18:22Z

up vote 3 down vote accepted

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

answered Sep 30 '12 at 14:18

Ayman Hourieh
11.8k21643

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

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