Prove this formula $1+\cos\theta+\cos2\theta+...+\cos n\theta=\frac{1}{2}+\frac{\sin(n+\frac{1}{2})\theta}{2\sin\frac{\theta}{2}}$ [duplicate]

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This is homework but I’m really stuck. The question is to prove a fromula which states:

$$1+\cos\theta+\cos2\theta+...+\cos n\theta=\frac{1}{2}+\frac{\sin(n+\frac{1}{2})\theta}{2\sin\frac{\theta}{2}}$$

I want to solve it using complex numbers So I came to this (I missed Re in last one) Can you guys please help me finish this ?

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1 Answer

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You can refer this :

👉 For more insights, check out this resource.

This way you can easily do to prove Lagrange’s trigonometric identity:

original answer

👉 Discover more in this in-depth guide.

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