A. \(x \ne \pi + k3\pi ,\left( {k \in Z} \right)\)
B. \(x \ne - \frac{\pi }{{12}} + k3\pi ,\left( {k \in Z} \right)\)
C. \(x \ne - \frac{\pi }{2} + k6\pi ,\left( {k \in Z} \right)\)
D. \(x \ne \pi + k6\pi ,\left( {k \in Z} \right)\)
A
\(\begin{array}{l}
y = \tan \left( {\frac{x}{3} + \frac{\pi }{6}} \right) = \frac{{\sin \left( {\frac{x}{3} + \frac{\pi }{6}} \right)}}{{{\rm{cos}}\left( {\frac{x}{3} + \frac{\pi }{6}} \right)}}\\
\Leftrightarrow {\rm{cos}}\left( {\frac{x}{3} + \frac{\pi }{6}} \right) \ne 0 \Leftrightarrow {\rm{cos}}\left( {\frac{x}{3} + \frac{\pi }{6}} \right) \ne c{\rm{os}}\frac{\pi }{2}\\
\Leftrightarrow \frac{x}{3} + \frac{\pi }{6} \ne \frac{\pi }{2} + k\pi \Leftrightarrow x \ne \pi + k3\pi \left( {k \in Z} \right)
\end{array}\)
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