Prove that \( \cos \alpha+\cos (\alpha+\beta)+\cos (\alpha+2 \beta)+\ldots+\cos \)
\[
(\alpha+(n...
Prove that \( \cos \alpha+\cos (\alpha+\beta)+\cos (\alpha+2 \beta)+\ldots+\cos \)
\[
(\alpha+(n-1) \beta)=\frac{\cos \left\{\alpha+\left(\frac{n-1}{2}\right) \beta\right\} \sin \left(\frac{n \beta}{2}\right)}{\sin \frac{\beta}{2}}
\]
for all \( n \in N \).
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