>>>>> "Juan" == Juan Pablo Carbajal <carbajal at ifi.uzh.ch> writes:
Juan> There are the functions trigreduce and trigsimp. However,
Juan> 1. "A" and "B" are just constants for Maxima, there is no way it can
Juan> self-generate A=cos(c), B=-sin(c).
Juan> 2. The expression you sent is not always true, it holds only if -1<A<1
Juan> and -1<B<1.
Juan> Hence, if you know inequalities in 2. are true, then there exist a
Juan> value c, such that 1. is valid. If you assume all this then
But if you divide the expression by sqrt(A^2+B^2), I think you will be
able to write the result in the desired form where
A=sqrt(A^2+B^2)*cos(c) and B = sqrt(A^2+B^2)*sin(c).
Juan> trigreduce( subst([A=cos(c), B=-sin(c)], A*cos(w*t)+B*sin(w*t)) )
I didn't check to see if maxima is smart enough to give the expected
answer with the division, but it can obviously be done by hand.
Ray