Prove that:
\[
(\cos \alpha+\cos \beta)^{2}+(\sin \alpha+\sin \beta)^{2}=4 \cos ^{2}\left(\frac{...
Prove that:
\[
(\cos \alpha+\cos \beta)^{2}+(\sin \alpha+\sin \beta)^{2}=4 \cos ^{2}\left(\frac{\alpha-\beta}{2}\right)
\]
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