Đáp án:
Giải thích các bước giải:
$\begin{array}{l}
\cos \left( {5x + 2} \right) = \sin \left( {\frac{\pi }{3} - x} \right) = \cos \left( {\frac{\pi }{2} - \frac{\pi }{3} + x} \right)\\
\Leftrightarrow \cos \left( {5x + 2} \right) = \cos \left( {\frac{\pi }{6} + x} \right)\\
\Leftrightarrow \left[ \begin{array}{l}
5x + 2 = \frac{\pi }{6} + x + k2\pi \\
5x + 2 = - \frac{\pi }{6} - x + k2\pi
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
4x = \frac{\pi }{6} - 2 + k2\pi \\
6x = - \frac{\pi }{6} - 2 + k2\pi
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = \frac{\pi }{{24}} - \frac{1}{2} + \frac{{k\pi }}{2}\\
x = - \frac{\pi }{{36}} - \frac{1}{3} + \frac{{k\pi }}{3}
\end{array} \right.
\end{array}$