Giải các phương trình lượng giác sau: a) 2cosx + căn bậc hai 3 = 0

a)

\(2\cos x + \sqrt 3  = 0\)

\[ \Leftrightarrow \cos x =  - \frac{{\sqrt 3 }}{2} \Leftrightarrow \cos x = \cos \frac{{5\pi }}{6}\]

\[ \Leftrightarrow \left[ \begin{array}{l}x = \frac{{5\pi }}{6} + k2\pi \\x =  - \frac{{5\pi }}{6} + k2\pi \end{array} \right.\left( {k \in \mathbb{Z}} \right) =  > S = \left\{ { \pm \frac{{5\pi }}{6} + k2\pi } \right\}.\]

b)

\( \Leftrightarrow \sin 2x = \cos \left( {x + \frac{\pi }{3}} \right) \Leftrightarrow \cos \left( {\frac{\pi }{2} - 2x} \right) = \cos \left( {x + \frac{\pi }{3}} \right) \Leftrightarrow \left[ \begin{array}{l}\frac{\pi }{2} - 2x = x + \frac{\pi }{3} + k2\pi \\\frac{\pi }{2} - 2x =  - \left( {x + \frac{\pi }{3}} \right) + k2\pi \end{array} \right.\)

\( \Leftrightarrow \left[ \begin{array}{l} - 3x =  - \frac{\pi }{6} + k2\pi \\ - x =  - \frac{{5\pi }}{6} + k2\pi \end{array} \right. \Leftrightarrow \left[ \begin{array}{l}x = \frac{\pi }{{18}} + \frac{{k2\pi }}{3}\\x = \frac{{5\pi }}{6} + k2\pi \end{array} \right.(k \in Z)\)