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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.

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  • $\begingroup$ can you show your initial code, so we try to help! $\endgroup$ – Alrubaie Apr 6 '19 at 17:00
  • $\begingroup$ Try Collect[exp /. Cos[x n_.] -> x^n, x]/. x^n_. -> Cos[n x]. $\endgroup$ – Somos Apr 7 '19 at 2:29
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is this what you are asking? 

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

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

{3, 5, 12}

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  • $\begingroup$ Yes, thanks this is it! $\endgroup$ – Riccardo Apr 6 '19 at 17:28
  • $\begingroup$ you are welcome! $\endgroup$ – J42161217 Apr 6 '19 at 17:35

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