Sum to Product

Sum to product formula: sin A − sin B

sinAsinB=2cosA+B2sinAB2\sin A - \sin B = 2 \cos\tfrac{A+B}{2} \sin\tfrac{A-B}{2}

sin A − sin B = 2 cos((A + B)/2) sin((A − B)/2). The sine and cosine swap places compared with the sum version - the half-sum takes the cosine and the half-difference takes the sine.

Related Sum to Product identities

Common questions

What is the sin A − sin B identity?

sin A − sin B = 2 cos((A + B)/2) sin((A − B)/2). The sine and cosine swap places compared with the sum version - the half-sum takes the cosine and the half-difference takes the sine.

Which identities are related to sin A − sin B?

sin A − sin B belongs to the Sum to Product group. The identities used alongside it most often are sin A + sin B, cos A + cos B and cos A − cos B.

Practise it

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