What is cos2x times cosx?

The expression ( \cos(2x) \cdot \cos(x) ) can be simplified using the double angle identity for cosine. Specifically, ( \cos(2x) = 2\cos^2(x) - 1 ). Thus, multiplying gives ( \cos(2x) \cdot \cos(x) = (2\cos^2(x) - 1) \cdot \cos(x) = 2\cos^3(x) - \cos(x) ).