Let . Which of the following describes the domain of…

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

Problem

Let f(x)=sec⁡x1+tan⁡xf(x)=\dfrac{\sec x}{1+\tan x}. Which of the following describes the domain of f(x)f(x)? (a) x≠(2n+1)π2,  n∈Zx\neq\left(2n+1\right)\dfrac{\pi}{2},\;n\in\mathbb{Z} (b) x≠(2n+1)π2 and   x≠−π4+nπ,  n∈Zx\neq\left(2n+1\right)\dfrac{\pi}{2}\text{ and }\;x\neq-\dfrac{\pi}{4}+n\pi,\;n\in\mathbb{Z} (c) x≠(2n+1)π2 and x≠π4+nπ,  n∈Zx\neq\left(2n+1\right)\dfrac{\pi}{2}\text{ and }x\neq\dfrac{\pi}{4}+n\pi,\;n\in\mathbb{Z} (d) x≠−π4+nπ,  n∈Zx\neq-\dfrac{\pi}{4}+n\pi,\;n\in\mathbb{Z}

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