I'm assuming we're solving for coefficients and .
We know .
Solve the second equation and plug the answer into the first equation.
After you simplify shift one of the cos terms to the other side and determine what the relationship is.
Here I have a trigonometric equation, where a, A, b, and B are constants. This equation needs to be solved for x.
0 = a*cos(Ax)+b*cos(Bx)
If the second equation below could be solved for x, that would also solve the problem. Solving one will lead to a solution for the other.
I will use different constants than above to avoid confusion.
G*x = arccos(H*cos(x))