Product to Sum

Product to sum formula: cos α cos β

cosαcosβ=12[cos(αβ)+cos(α+β)]\cos\alpha \cos\beta = \tfrac{1}{2}[\cos(\alpha-\beta) + \cos(\alpha+\beta)]

cos α cos β = ½[cos(α − β) + cos(α + β)]. Both terms carry a plus sign here, unlike the sine-times-sine version. It comes straight from adding the cosine sum and difference formulas.

Related Product to Sum identities

Practise it

Reading a formula is not the same as recalling it under time pressure. The workspace drills Product to Sum questions in the quiz, and the triangle solver shows a worked solution for any triangle you type in.

Or browse all 45 identities in the full reference, or read the trigonometry guides for the method behind them.