Trigonify

Sum to Product

Sum to product formula: sin A − sin B

sin⁡A−sin⁡B=2cos⁡A+B2sin⁡A−B2\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

sin A + sin Bcos A + cos Bcos 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.

Practise Sum to ProductOpen the triangle solver

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