Unfortunately, this simplification is not yet implemented in SymPy (though the reverse is, see expand(trig=True)). See http://code.google.com/p/sympy/issues/detail?id=1590.
It shouldn't be too hard to implement, though, you just need to implement the series expansions given at http://en.wikipedia.org/wiki/Trig_identities#Power-reduction_formula. Actually, there is another way that you can do it, which involves taking advantage of the complex exponential form of sine and cosine. You would do something like this: In [3]: (cos(x)**5).rewrite(exp).expand().rewrite(cos) Out[3]: cos(5⋅x) 5⋅cos(x) 5⋅cos(3⋅x) ──────── + ──────── + ────────── 16 8 16 Aaron Meurer On Nov 19, 2010, at 6:26 AM, Javier wrote: > Hi all, > > Anyone knows if there is a simple way of doing an expansion of > sin(x)**p and cos(x)**p as a sum of cos(ix) or sin(ix) in sympy. I > currently can do it in maple with the combine command but I want to > use sympy. > > > The idea is that for example: > > sin(x)**5 = 1/16 sin(5 x) - 5/16 sin(3 x) + 5/8 sin(x) > cos(x)**5 = 1/16 cos(5 x) + 5/16 cos(3 x) + 5/8 cos(x) > > Can anyone help me please? > > Thanks in advance > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To post to this group, send email to sy...@googlegroups.com. > To unsubscribe from this group, send email to > sympy+unsubscr...@googlegroups.com. > For more options, visit this group at > http://groups.google.com/group/sympy?hl=en. > -- You received this message because you are subscribed to the Google Groups "sympy" group. To post to this group, send email to sy...@googlegroups.com. To unsubscribe from this group, send email to sympy+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sympy?hl=en.
