Determine the domain of .

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

Problem

Determine the domain of

f(x)=\sec\!\left(2x-\dfrac{\pi}{3}\right)

. (a)

\mathbb{R}\setminus\left\{x=\dfrac{\pi}{6}+\dfrac{n\pi}{2},\;n\in\mathbb{Z}\right\}

(b)

\mathbb{R}\setminus\left\{x=\dfrac{\pi}{3}+\dfrac{n\pi}{2},\;n\in\mathbb{Z}\right\}

(c)

\mathbb{R}\setminus\left\{x=\dfrac{5\pi}{12}+\dfrac{n\pi}{2},\;n\in\mathbb{Z}\right\}

(d)

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