Solution of $\cos(2x) - A\sin(2x) = 0?$

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The physics exercises of today's lecture made me face following equation:

$$\cos(2x) - A\sin(2x) = 0$$

I was not able to solve for $x$? Do you know how to proceed?

(Note: A is $\approx -1/7$)

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You can rearrange to get $$\tan(2x)=\frac{1}{A}\,.$$ The general solution is $$x=\frac{1}{2}\arctan\left(\frac{1}{A}\right)+\frac{n\pi}{2},$$ where $n$ is an integer.