Cosine addition.
$$\tag{1}
\cos a + \cos b = 2 \cos \tfrac12(a + b) \cos \tfrac12(a - b)
$$
$$\tag{2}
\cos \tfrac12(a + b) \cos \tfrac12(a - b) = \tfrac12 \cos a + \tfrac12 \cos b
$$
$$\tag{3}
\cos \alpha \cos \beta = \tfrac12 \cos (\alpha + \beta) + \tfrac12 \cos (\alpha - \beta)
$$
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