Sum to Product

Sum to product formula: cos A − cos B

cosAcosB=2sinA+B2sinAB2\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

Common questions

What is the cos A − cos B identity?

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.

Which identities are related to cos A − cos B?

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