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