Solve $cos 4 x = cos 2 x$

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Solution

$cos 4 x = cos 2 x \Rightarrow cos 4 x - cos 2 x = 0 \Rightarrow 2 (sin \frac{4 x + 2 x}{2} sin \frac{2 x - 4 x}{2}) = 0 \Rightarrow - 2 (sin 3 x sin x) = 0 \Rightarrow sin 3 x = 0, sin x = 0 \Rightarrow x = \frac{n π}{3}, x = n π$

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