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Sum to Product Calculator

Convert sums of sines and cosines to products using sum-to-product formulas.

Calculator

Sum/Difference Type

Unit

DegreesRadians

Angle A

Angle B

All Sum-to-Product Formulas

sin A + sin B = 2·sin((A+B)/2)·cos((A-B)/2)

sin A - sin B = 2·cos((A+B)/2)·sin((A-B)/2)

cos A + cos B = 2·cos((A+B)/2)·cos((A-B)/2)

cos A - cos B = -2·sin((A+B)/2)·sin((A-B)/2)

Key: The arguments become half-sum and half-difference: (A+B)/2 and (A-B)/2.

Frequently Asked Questions

When do I use sum-to-product formulas?

When solving equations like sin A + sin B = 0, or when you need to factor a trig expression. Converting to a product often makes it easier to find zeros.

How do I remember these formulas?

The result always has one argument (A+B)/2 and one (A-B)/2. Sums of sines/cosines give sin·cos or cos·cos. Note the negative sign for cos A - cos B.

Related Calculators

Product to Sum Sum & Difference Half Angle Trig Equations

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