Sine sum and difference formula: sin(α ± β) = sin α cos β ± cos α sin β
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
Common questions
What is the sin(α ± β) identity?
sin(α ± β) = sin α cos β ± cos α sin β. The signs match: a plus inside gives a plus outside.
When do you use the sin(α ± β) identity?
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.
Which identities are related to sin(α ± β)?
sin(α ± β) belongs to the Sum & Difference group. The identities used alongside it most often are cos(α ± β) and tan(α ± β).
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.