If =17 3 then - = - Vidyadip

MCQ

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

A
$\frac{1}{2 \sqrt{3}}$
B
$\frac{-1}{2 \sqrt{3}}$
C
$\frac{2}{\sqrt{3}}$
✓
$-\frac{2}{\sqrt{3}}$

✓

Answer

Correct option: D.

$-\frac{2}{\sqrt{3}}$

Given, $\theta=\frac{17 \pi}{3}=\frac{18 \pi-\pi}{3} $
$\Rightarrow \theta=6 \pi-\frac{\pi}{3}$
Now, $\tan \theta-\cot \theta=\tan \theta-\frac{1}{\tan \theta}$
$=\tan \left(6 \pi-\frac{\pi}{3}\right)-\frac{1}{\tan \left(6 \pi-\frac{\pi}{3}\right)}$
$=\tan \left(-\frac{\pi}{3}\right)-\frac{1}{\tan \left(-\frac{\pi}{3}\right)}$
$=-\sqrt{3}-\left(\frac{1}{-\sqrt{3}}\right)$
$=\frac{-2}{\sqrt{3}}$

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