Product to Sum

Product to sum formula: sin α cos β

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

sin α cos β = ½[sin(α + β) + sin(α − β)]. Products of trig functions are awkward to integrate and to graph; sums are not. This is also the identity behind acoustic beats, where two close frequencies multiply into a slow envelope.

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.