$c o s 3 x + c o s x - c o s 2 x = 0$

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Solution

$c o s 3 x + c o s x - c o s 2 x = 0 2 c o s (\frac{3 x + x}{2}) c o s (\frac{3 x - x}{2}) - c o s 2 x = 0 c o s 2 x (2 c o s x - 1) = 0 i f c o s 2 x = 0 t h e n 2 x = (2 n + 1) (\frac{π}{2}) ∴ x = (2 n + 1) (\frac{π}{4}) i f 2 c o s x - 1 = 0 o r c o s x = (\frac{1}{2}) = c o s (\frac{π}{3}) ∴ x = 2 n π \pm (\frac{π}{3})$

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