Collect Fourier series terms

Question

Is there a way to make mathematica automatically collect terms like $\mathrm{Cos}[n\ x]$ with $n=1,2,3...$? I have a long expression coming out of a Fourier series where I see a lot of $Cos[x],Cos[2 x],Cos[3 x]$ and so on, but Simplify is very inefficient. I would like mathematica to automatically collect all coefficients of the various Cos[n x] without having to do it manually for each one of them.

Answer 1

is this what you are asking?

exp=3Cos[x]+5Cos[2x]+12Cos[3x];

Coefficient[exp,Cos[x #]]&/@Range@3

{3, 5, 12}