Trigonify

Sum to Product

Sum to product formula: sin A + sin B

sin⁡A+sin⁡B=2sin⁡A+B2cos⁡A−B2\sin A + \sin B = 2 \sin\tfrac{A+B}{2} \cos\tfrac{A-B}{2}

sin A + sin B = 2 sin((A + B)/2) cos((A − B)/2). Going from a sum to a product is what lets you solve equations by factoring: a product is zero when either factor is, so the whole solution set falls out at once.

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.