(i) State the condition on for which is defined. (ii) Using the result of part (i),…

MATHEMATICS · Subjective · A Level · Mathematics · Trigonometry · Trigonometry

Problem

(i) State the condition on

\cos x

for which

\tan x

is defined. (ii) Using the result of part (i), explain why the points

x=(2n+1)\,\dfrac{\pi}{2}

n\in\mathbb Z

, do not belong to the domain of

\tan x

. (iii) Evaluate the one–sided limits

\lim_{x\to\left(\tfrac{\pi}{2}\right)^-}\tan x\quad\text{and}\quad\lim_{x\to\left(\tfrac{\pi}{2}\right)^+}\tan x

and hence show that the graph of

\tan x

possesses a vertical asymptote at

x=\dfrac{\pi}{2}