2cosAcosB

The trigonometric identity 2cosAcosB is a product-to-sum formula used in trigonometry and calculus. It relates the product of two cosine functions to a sum of cosine functions. The formula states that 2cosAcosB is equal to cos(A + B) + cos(A - B). This identity can be derived from the angle addition and subtraction formulas for cosine.

Specifically, recall that cos(A + B) = cosAcosB - sinAsinB and cos(A - B) = cosAcosB + sinAsinB. If we add these two equations together, the sinAsinB terms cancel out, leaving us with cos(A + B) + cos(A - B) = 2cosAcosB. This transformation is particularly useful for simplifying expressions involving products of trigonometric functions or for integrating such products. It allows for the conversion of a product into a form that is often easier to manipulate or evaluate. The identity holds true for all real values of angles A and B.