Giải phương trình: cos2x – 3cosx + 2 = 0.

cos2x – 3cosx + 2 = 0 \( \Leftrightarrow 2{\cos ^2}x - 1 - 3\cos x + 2 = 0\)

\( \Leftrightarrow 2{\cos ^2}x - 3\cos x + 1 = 0 \Leftrightarrow \left[ {\begin{array}{*{20}{c}}{\cos x = 1}\\{\cos x = \frac{1}{2} = \cos \frac{\pi }{3}}\end{array}} \right. \Leftrightarrow \left[ {\begin{array}{*{20}{c}}{x = k2\pi }\\{x = \pm \frac{\pi }{3} + k2\pi }\end{array}} \right.\left( {k \in \mathbb{Z}} \right)\).

Vậy \(S = \left\{ {k2\pi ; \pm \frac{\pi }{3} + k2\pi ,\,k \in \mathbb{Z}} \right\}\).