Convert the following sums or differences into products cos 12 alpha + cos 8 alpha?

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Solution

$\cos 12 α + \cos 8 α = 2 \cos (\frac{12 α + 8 α}{2}) \cos (\frac{12 α - 8 α}{2}) [as, \cos C + \cos D = 2 \cos (\frac{C + D}{2}) . \cos (\frac{C - D}{2})] = 2 \cos (\frac{20 α}{2}) . \cos (\frac{4 α}{2}) = 2 \cos 10 α . \cos 2 α$

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