Sum & Difference

Sine sum and difference formula: sin(α ± β) = sin α cos β ± cos α sin β

sin(α±β)=sinαcosβ±cosαsinβ\sin(\alpha \pm \beta) = \sin\alpha \cos\beta \pm \cos\alpha \sin\beta

sin(α ± β) = sin α cos β ± cos α sin β. The signs match: a plus inside gives a plus outside. Use it to get exact values for angles you can build from known ones - sin 75° = sin(45° + 30°) - and to derive the double-angle formula by setting β = α.

Related Sum & Difference identities

Practise it

Reading a formula is not the same as recalling it under time pressure. The workspace drills Sum & Difference 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.