Đáp án:
Giải thích các bước giải:
\(\begin{array}{l}
a.2\cos 2x + \cos x - 3 = 0\\
\to 2(2{\cos ^2}x - 1) + \cos x - 3 = 0\\
\to \left[ \begin{array}{l}
\cos x = 1\\
\cos x = \frac{{ - 5}}{4}(l)
\end{array} \right. \to x = k2\pi \\
b.\frac{{\sqrt 3 }}{2}\sin x + \frac{1}{2}\cos x = \frac{{\sqrt 3 }}{2}\\
\to \cos \frac{\pi }{6}.\sin x + \sin \frac{\pi }{6}.\cos x = \frac{{\sqrt 3 }}{2}\\
\to \sin (x - \frac{\pi }{6}) = \frac{{\sqrt 3 }}{2}\\
\to \left[ \begin{array}{l}
x - \frac{\pi }{6} = \frac{\pi }{3} + k2\pi \\
x - \frac{\pi }{6} = \frac{{2\pi }}{3} + k2\pi
\end{array} \right. \to \left[ \begin{array}{l}
x = \frac{\pi }{2} + k2\pi \\
x = \frac{{5\pi }}{6} + k2\pi
\end{array} \right.\\
\end{array}\)
