Trig functions in CAS

[Eddie W. Shore]

You probably just have to play around the CAS commands. I don't think there is a built in function that breaks down sin(6x) to sin(3x + 3x).

The trigexpand command will expand such expressions as cos(nx) and sin(nx) into a polynomial. Using tcollect I was able to go the other way:

tcollect(2*sin(3x)*cos(3x)) -> sin(6x)

trigexpand(sin(6x)) -> (32*cos^5 x - 32*cos^3 + 6*cos x)*sin x