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Sum to Product

Sum to product formula: cos A − cos B

cos⁡A−cos⁡B=−2sin⁡A+B2sin⁡A−B2\cos A - \cos B = -2 \sin\tfrac{A+B}{2} \sin\tfrac{A-B}{2}

cos A − cos B = −2 sin((A + B)/2) sin((A − B)/2). The leading minus sign is the one people drop: a difference of cosines becomes a negative product of sines, not a positive one.

Related Sum to Product identities

sin A + sin Bsin A − sin 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.