Solving a general complex trigonometric equation

[omertech]

Hello everyone!

Homework Statement

Solving a relatively general equation representing a constant combination of 2 trigonometric functions.

Homework Equations

$$a\cos{(vx+p)}+b\cos{(ux+q)}=c$$

The Attempt at a Solution

I really don't have any idea for a general solution to this equation..

Best Regards

 

[haruspex]

Not aware of any general analytic solution. Do you have a reason for believing such exists?