Product: cos A cos B

This identity rewrites a product of two cosine terms as the average of two cosine waves: one with the difference of the angles and one with their sum. It comes from expanding cos(A−B) and cos(A+B) using the angle addition formulas, then adding the results so the sine terms cancel. The result is useful because products of trig functions are often easier to simplify, integrate, or analyze when converted into sums.

Use this when you need to simplify trig expressions, especially in integration, Fourier-style signal manipulation, or solving equations involving products of cosines. It is also helpful when combining oscillations or finding beat patterns in waves and vibrations.

• Swapping the signs and writing cos(A+B) - cos(A-B) instead of a sum
• Forgetting the factor of 1/2 in front of the bracket
• Using the formula with angles in mixed units or miscalculating the sum and difference angles