Find the domain of the function .

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

Problem

Find the domain of the function

h(x)=\dfrac{\sec(4x-\pi)}{\tan(2x)}

. (a)

\mathbb{R}\setminus\left\{x=\dfrac{\pi}{4}+\dfrac{n\pi}{2},\,x=\dfrac{3\pi}{8}+\dfrac{n\pi}{4},\,n\in\mathbb{Z}\right\}

(b)

\mathbb{R}\setminus\left\{x=\dfrac{n\pi}{2},\,x=\dfrac{\pi}{4}+\dfrac{n\pi}{2},\,x=\dfrac{3\pi}{8}+\dfrac{n\pi}{4},\,n\in\mathbb{Z}\right\}

(c)

\mathbb{R}\setminus\left\{x=\dfrac{n\pi}{2},\,x=\dfrac{\pi}{4}+\dfrac{n\pi}{2},\,x=\dfrac{\pi}{8}+\dfrac{n\pi}{4},\,n\in\mathbb{Z}\right\}

(d)

\mathbb{R}\setminus\left\{x=n\pi,\,x=\dfrac{\pi}{4}+\dfrac{n\pi}{2},\,x=\dfrac{3\pi}{8}+\dfrac{n\pi}{4},\,n\in\mathbb{Z}\right\}