I am attempting to combine the sum of two sinusoids having the same frequency in Maple (e.g. A*cos(10*x) + B*sin(10*x + Pi/3) = M*cos(10*x + phi) )

The long way through this is to break each term up into cartesian components and add them (x = A + B*cos(Pi/3 + 3*Pi/2) , y = B*sin(Pi/3 + 3*Pi/2) ). Following the summation, they can be converted back to polar (M = sqrt( x^2 + y^2 ) and phi = arctan(y/x)).

This is a long process for me and if my graphing calculator...