I notice there are actually two standard forms of trignometric polynomials:
$ c_0+ \sum_{k=1}^n \sum_{\alpha +\beta =k} c_{\alpha ,\beta}\sin^\alpha(x) \cos^\beta(x)$
$ c_0+\sum_{k=1}^n\{a_k\sin(kx) +b_k\cos(kx)\}$
I know how to convert form 2 to 1. But generally how can I convert 1 to 2?