# Simplify a series expansion including trigonometric expressions

I have the expression

Maf P ωm Sin[P t ωm]
((3 Vm)/(π R) +
Sum[
-((6 (-1)^k Vm Cos[k p t w])/((-π + 36 k^2 π) * Sqrt[R^2 + k^2 L^2 p^2 w^2])),
{k, 1, n}])


and I would like to have Mathematica automatically simplify it to expressions like Sin[k p t w + P t ωm] and Sin[k p t w - P t ωm]. How can I do that?

• You can use TrigReduce[Sin[P t ωm] Cos[k p t w] ] – yarchik Sep 19 at 13:46