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Product-to-sum identities

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sinα cosβ
½ [sin(α+β) + sin(α-β)]
cosα sinβ
½ [sin(α+β) - sin(α-β)]
cosα cosβ
½ [cos(α+β) + cos(α-β)]
sinα sinβ
-½ [cos(α+β) - cos(α-β)]