Simplify
\(\cos(\alpha+\beta)+\cos(\alpha-\beta)\).
Solution
Use \(\cos(u\pm v)=\cos u\cos v\mp\sin u\sin v\):
\(
\cos(\alpha+\beta)+\cos(\alpha-\beta)\)
\( =(\cos\alpha\cos\beta-\sin\alpha\sin\beta)\)
\(+(\cos\alpha\cos\beta+\sin\alpha\sin\beta)\)
\(=2\cos\alpha\cos\beta.
\)
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