Question

Principle solution of equation $cotx=-\sqrt{3}$ is

• A. $\frac{\pi }{3}$
• B. $\frac{2\pi }{3}$
• C. $\frac{\pi }{6}$
• D. $\frac{5\pi }{6}$

Answer 1

The correct option is D $\frac{5\pi }{6}$

We have,

$\cot x=-\sqrt{3}$

We know that

$\cot (\pi -\theta )=-\cot \theta$

Therefore,

$\cot x=-\sqrt{3}=-\cot \frac{\pi }{6}$

$\cot x=\cot (\pi -\frac{\pi }{6})$

$\cot x=\cot \frac{5\pi }{6}$

$x=\frac{5\pi }{6}$

Hence, this is the answer.