For the function

MATHEMATICS · Single correct · A Level · Mathematics · Trigonometry · Trigonometry

Problem

For the function g(x)=tan⁡(3x+π6)csc⁡xg(x)=\tan\left(3x+\dfrac{\pi}{6}\right)\csc x, which of the following represents its domain? (a) R∖{x=nπ,  n∈Z}\mathbb{R}\setminus\{x=n\pi,\;n\in\mathbb{Z}\} (b) R∖{x=nπ or x=π9+nπ3,  n∈Z}\mathbb{R}\setminus\{x=n\pi\text{ or }x=\dfrac{\pi}{9}+\dfrac{n\pi}{3},\;n\in\mathbb{Z}\} (c) R∖{x=π9+nπ,  n∈Z}\mathbb{R}\setminus\{x=\dfrac{\pi}{9}+n\pi,\;n\in\mathbb{Z}\} (d) R∖{x=π6+nπ3,  n∈Z}\mathbb{R}\setminus\{x=\dfrac{\pi}{6}+\dfrac{n\pi}{3},\;n\in\mathbb{Z}\}

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