Trigonify

Topics · 4 identities

Sum to Product

Turning sums and differences of sines and cosines into products.

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}
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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}
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cos A + cos B

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