Producttosum
Product-to-sum refers to a set of trigonometric identities that convert products of sine and cosine into sums of trigonometric functions with the sum and difference of the original angles. These formulas are derived from the addition formulas for sine and cosine and are used to simplify integration, series, and other trigonometric expressions.
The standard identities include:
- cos A cos B = 1/2 [cos(A+B) + cos(A-B)]
- sin A sin B = 1/2 [cos(A-B) - cos(A+B)]
- sin A cos B = 1/2 [sin(A+B) + sin(A-B)]
These identities allow any product of sine and cosine to be rewritten as a sum of functions
General use and applications: for any real angles A and B, a product such as sin A
Derivation and relation to other identities: the product-to-sum formulas follow from the addition formulas sin(A±B) and