Giải phương trình cos ( 3 x − pi/ 6 ) = 1/ 2

ĐK: \(x \in \mathbb{R}\).

Ta có: \(\cos \left( {3x - \frac{\pi }{6}} \right) = \frac{1}{2} \Leftrightarrow \cos \left( {3x - \frac{\pi }{6}} \right) = \cos \left( {\frac{\pi }{3}} \right) \Leftrightarrow \left[ {\begin{array}{*{20}{c}}{3x - \frac{\pi }{6} = \frac{\pi }{3} + k2\pi }\\{3x - \frac{\pi }{6} =  - \frac{\pi }{3} + k2\pi }\end{array}} \right.,\left( {k \in \mathbb{Z}} \right)\)     \( \Leftrightarrow \left[ {\begin{array}{*{20}{c}}{x = \frac{\pi }{6} + \frac{{k2\pi }}{3}}\\{x =  - \frac{\pi }{{18}} + \frac{{k2\pi }}{3}}\end{array}} \right.\,\,\,,\,\left( {k \in \mathbb{Z}} \right)\).

Vậy nghiệm của phương trình là: \(\left[ {\begin{array}{*{20}{c}}{x = \frac{\pi }{6} + \frac{{k2\pi }}{3}}\\{x =  - \frac{\pi }{{18}} + \frac{{k2\pi }}{3}}\end{array}} \right.\,\,,\,\,\left( {k \in \mathbb{Z}} \right)\)