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**My book's throwing equations out of nowhere!!!**

On proving one theorem, my book says:

[tex]1 + 2\sum_{k = 1} ^ {n} \cos k \alpha = \frac{\sin \left( n + \frac{1}{2} \right) \alpha}{\sin \frac{\alpha}{2}}[/tex]

I have no idea where that formula comes from , and I tried in vain proving it, but I failed. Can anybody gives me a hint?

Thank you,

Any help will be appreciated,

Viet Dao,

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