<s>[INST] Solve a trigonometric equation: $|1-2\sin^2 x|=|\cos x|$ I have difficulty in solving this equation:
$$|1-2\sin^2 x|=\lvert\cos x\rvert.$$
What are the indications to solve the exercise correctly?
 [/INST] $1 - 2\sin^2 x = 2\cos^2 x - 1\\
2\cos^2 x  - 1 = \pm \cos x\\
2\cos^2 x  \pm\cos x - 1 = 0$
Apply the quadratic formula:
$\cos x = \pm \frac 14 \pm \frac 34\\
\cos x = \pm \frac 12, \pm 1 $
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