quantum mechanics - Momentum of wave function with sum of cosines

I am struggling with question about possible outcomes of momentum measurement and their probability. I know I can calculate it with momentum operator, but a wavefunction is of form

$$\psi (x)=3\cos\pi x+\cos3\pi x$$

and I am unsure how to deal with it, as the derivative consists of sines.

I know that $\cos{kx}=\frac{e^{ikx}+e^{−ikx}}{2}$ and $p_{x}=\hbar k$, but does it mean that the momentum is sum of eigenvalues of individual exponentials?