Đáp án:
f. \(x \ne \dfrac{{5\pi }}{{18}} + \dfrac{{k\pi }}{3}\)
Giải thích các bước giải:
\(\begin{array}{l}
f.DK:\cos \left( {3x - \dfrac{\pi }{3}} \right) \ne 0\\
\to 3x - \dfrac{\pi }{3} \ne \dfrac{\pi }{2} + k\pi \\
\to 3x \ne \dfrac{{5\pi }}{6} + k\pi \\
\to x \ne \dfrac{{5\pi }}{{18}} + \dfrac{{k\pi }}{3}\left( {k \in Z} \right)\\
g.DK:\left\{ \begin{array}{l}
\cos 2x \ne 0\\
\sin x \ne - 1\\
\sin \left( {3x + \dfrac{\pi }{6}} \right) \ne 0
\end{array} \right.\\
\to \left\{ \begin{array}{l}
2x \ne \dfrac{\pi }{2} + k\pi \\
x \ne - \dfrac{\pi }{2} + k2\pi \\
3x + \dfrac{\pi }{6} \ne k\pi
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x \ne \dfrac{\pi }{4} + \dfrac{{k\pi }}{2}\\
x \ne - \dfrac{\pi }{2} + k2\pi \\
x \ne - \dfrac{\pi }{{18}} + \dfrac{{k\pi }}{3}
\end{array} \right.\left( {k \in Z} \right)
\end{array}\)
