Problem

$2 \cos ^{2} x-\cos x=0$

Answer

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Answer

\(\boxed{x = \frac{\pi}{3}, \frac{\pi}{2}, \frac{3\pi}{2}, \frac{5\pi}{3}}\)

Steps

Step 1 ：Factor out \(\cos x\) from the equation: \(2 \cos ^{2} x - \cos x = 0\) becomes \((2\cos x - 1)\cos x = 0\)

Step 2 ：Solve for x: \(x = \frac{\pi}{3}, \frac{\pi}{2}, \frac{3\pi}{2}, \frac{5\pi}{3}\)

Step 3 ：\(\boxed{x = \frac{\pi}{3}, \frac{\pi}{2}, \frac{3\pi}{2}, \frac{5\pi}{3}}\)

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