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I was wondering if there is a simple way to solve for the roots of a complicated summation of trig functions that can't be combined with any simple identities.

I have an equation of the form:

0 = sin(8x-arctan(4/3))+3.2sin(16x+pi/2)

where the two sines have different amplitudes, phases and a frequency that differs by a factor of 2. I would like to find the values of x on [0,pi/2] that satisfy this condition. I don't know very much about Fourier analysis but is there some method for solving this?

I need an analytical solution - not an approximation

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# Linear Combinations of Trig Functions - Finding Roots

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