Mathematics

Problem

For the function

g(x)=\tan\left(3x+\dfrac{\pi}{6}\right)\csc x

, which of the following represents its domain? a)

\mathbb{R}\setminus\{x=n\pi,\;n\in\mathbb{Z}\}

\mathbb{R}\setminus\{x=n\pi\text{ or }x=\dfrac{\pi}{9}+\dfrac{n\pi}{3},\;n\in\mathbb{Z}\}

\mathbb{R}\setminus\{x=\dfrac{\pi}{9}+n\pi,\;n\in\mathbb{Z}\}

\mathbb{R}\setminus\{x=\dfrac{\pi}{6}+\dfrac{n\pi}{3},\;n\in\mathbb{Z}\}