Product To Sum Formulas

About Product To Sum Formulas

The product of sine and cosine functions is expressed as a sum using the product to sum formulas. These are generated from trigonometry's sum and difference formulas. When solving the integrals of trigonometric functions, these formulas come in handy. The product-to-sum formulae are a series of trigonometric formulas that are derived from the sum and difference formulas, as we described in the previous section. The product to sum formulas is listed below, with their derivations shown below.

1. sin A cos B = (1/2) [ sin (A + B) + sin (A - B) ]
2. cos A sin B = (1/2) [ sin (A + B) - sin (A - B) ]
3. cos A cos B = (1/2) [ cos (A + B) - cos (A - B) ]
4. sin A sin B = (1/2) [ cos (A - B) + cos (A + B) ]

Product To Sum Formulas

As trigonometric identities, four formulas are commonly utilised.

• sin A cos B = (1/2) [ sin (A + B) + sin (A - B) ]
• cos A sin B = (1/2) [ sin (A + B) - sin (A - B) ]
• cos A cos B = (1/2) [ cos (A + B) - cos (A - B) ]
• sin A sin B = (1/2) [ cos (A - B) + cos (A + B) ]

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