I would just want to prove $\cos(t) + \cos(\pi t)$ is non periodic.
I don't know where to start it. Also I know that individually these signals ie $\cos(t)$ and $\cos(\pi t)$ are periodic with frequencies $1/(2 \pi)$ Hz and $1/2$ Hz respectively. But since the superpositon of these signals is not periodic should we represent them using Fourier transform only? What is the harm in drawing the frequency components at $1/(2 \pi)$ Hz and $1/2$ Hz using fourier series?