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Find all solutions of the following equations:
$\tan x = 0$
$2 \cos x + \sqrt{2} = 0$
$\cos^2 x - 1 = 0$
$2\cos^2 x - 3\cos x - 2 = 0$
$\tan^2 x + (\sqrt{3} - 1)\tan x - \sqrt{3} = 0$
$3\sec^2 x = \sec x$
$2\sin^2 x - \sin x - 1 = 0$
$\cos 2x = \sin x$
$\displaystyle{\frac{1+\cos x}{\cos x} = 2}$
$\displaystyle{\sqrt{\frac{1+2 \sin x}{2}} = 1}$
$\displaystyle{\cos^3 x - \cos x = 0}$
$\displaystyle{2 \cos 3x = 1}$
$\displaystyle{\cos^2 \theta + \sin \theta = \frac{5}{4}}$
$\displaystyle{2\sec^2 x - 5\tan x - 3 = 0}$
See full solutions.
$\pi n, \quad n \in \mathbb{Z}$
$\pm \frac{\pi}{4} + 2\pi n, \quad n \in \mathbb{Z}$
$\pi n, \quad n \in \mathbb{Z}$
$\pm \frac{2\pi}{3} + 2\pi n, \quad n \in \mathbb{Z}$
$\displaystyle{\left. \begin{array}{c} \frac{\pi}{4} + \pi n\\ \frac{2\pi}{3} + \pi n \end{array} \right\} \quad n \in \mathbb{Z}}$
no solutions
$\frac{\pi}{2} + \frac{2\pi}{3} n, \quad n \in \mathbb{Z}$
$\frac{\pi}{6} + \frac{2\pi}{3} n, \quad n \in \mathbb{Z}$
$2\pi n, \quad n \in \mathbb{Z}$
$\displaystyle{\left. \begin{array}{c} \frac{\pi}{6} + 2\pi n\\ \frac{5\pi}{6} + 2\pi n \end{array} \right\} \quad n \in \mathbb{Z}}$
$\frac{\pi}{2}n, \quad n \in \mathbb{Z}$
$\pm \frac{\pi}{9} + \frac{2\pi}{3} n, \quad n \in \mathbb{Z}$
$\displaystyle{\left. \begin{array}{c} \frac{\pi}{6} + 2\pi n\\ \frac{5\pi}{6} + 2\pi n \end{array} \right\} \quad n \in \mathbb{Z}}$
$\displaystyle{\left. \begin{array}{c} \textrm{arctan}\left(\frac{5+\sqrt{33}}{4}\right)+\pi n\\ \textrm{arctan}\left(\frac{5-\sqrt{33}}{4}\right)+\pi n \end{array} \right\} \quad n \in \mathbb{Z}}$