Where did the cosines come from?

Calculus Level 2

Let $\sum\limits_{n=0}^\infty a_n$ and $\sum\limits_{n=0}^\infty b_n$ be two convergent numerical series with positive terms.

True or false?:

The series $\sum\limits_{n=0}^\infty \left(a_n\cos(b_nx)+b_n\sin(a_nx) \right)$ is convergent in $\mathbb{R}$ .