Question

If $ \theta=\frac{17\,\pi}{3}$ then, $tan \, \theta - cot \, \theta = \ldots$

• A. $\frac{1}{2\sqrt{3}}$
• B. $\frac{-1}{2\sqrt{3}}$
• C. $\frac{2}{\sqrt{3}}$
• D. $-\frac{2}{\sqrt{3}}$

Answer 1

Answer: (D)

We have, $\theta=\frac{17 \pi}{3}$
$\therefore \tan \theta-\cot \theta =\tan \left(\frac{17 \pi}{3}\right)-\cot \left(\frac{17 \pi}{3}\right)$
$=\tan \left(5 \pi+\frac{2 \pi}{3}\right)-\cot \left(5 \pi+\frac{2 \pi}{3}\right)$
$=\tan \frac{2 \pi}{3}-\cot \frac{2 \pi}{3}$
$= \tan \left(\pi-\frac{\pi}{3}\right)-\cot \left(\pi-\frac{\pi}{3}\right)$
$=-\tan \pi / 3+\cot \pi / 3$
$=-\sqrt{3}+\frac{1}{\sqrt{3}}=\frac{-3+1}{\sqrt{3}}=\frac{-2}{\sqrt{3}}$