-cosx + căn 3 /3 sinx -1 =0 có tất cả các nghiệm là : giúp mk vs

Đáp án:

$\begin{array}{l}
 - \cos x + \frac{{\sqrt 3 }}{3}.\sin x - 1 = 0\\
 \Rightarrow  - \cos x + \frac{{\sqrt 3 }}{3}\sin x = 1\\
 \Rightarrow  - \frac{{\sqrt 3 }}{2}\cos x + \frac{1}{2}\sin x = \frac{{\sqrt 3 }}{2}\\
 \Rightarrow \cos \frac{{5\pi }}{6}.\cos x + \sin \frac{{5\pi }}{6}.\sin x = \frac{{\sqrt 3 }}{2}\\
 \Rightarrow \cos \left( {x - \frac{{5\pi }}{6}} \right) = \cos \frac{\pi }{6}\\
 \Rightarrow \left[ \begin{array}{l}
x - \frac{{5\pi }}{6} = \frac{\pi }{6} + k2\pi \\
x - \frac{{5\pi }}{6} =  - \frac{\pi }{6} + k2\pi 
\end{array} \right.\left( {k \in Z} \right)\\
 \Rightarrow \left[ \begin{array}{l}
x = \pi  + k2\pi \\
x = \frac{{2\pi }}{3} + k2\pi 
\end{array} \right.\left( {k \in Z} \right)
\end{array}$