Trigonometry
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Sum to Product: sin A − sin B

Sum-to-product identity.

Formula

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

Variables

A,BAngles

Did You Know?

This identity underlies the phenomenon of beats and the design of noise-cancelling headphones.

sum to productidentity