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As an example it is shown, how one convert a (simple) trigonometric equation into a polynomial problem and use Maple
to find a symbolic answer for the equation. The idea is to use the so called Joukowsky transform, which maps the circle
to the interval [-1, ... , +1].

I would have liked to simplify the result (as it is real in my case), but gave up. May be others have a good idea for that.

The problem came up in the thread www.mapleprimes.com/blog/williamfish/maximum, where one should find the
maximum of the expression 3*cos(4*Pi*x-1.3)+5*cos(2*Pi*x+0.5) for x in the unit interval (it is a periodic function).

Here is the file: www.mapleprimes.com/files/102_solving_a_trig_identity.mws
example convert

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