The principal value of $$\text{cot}^{-1}(\frac{-1}{\sqrt3})$$​ is:

Correct option is B

Given:

We are to find the principal value of:

​$$\cot^{-1}\left(-\frac{1}{\sqrt{3}}\right)$$​​

Concept Used:

​$$\cot^{-1}\left(\frac{1}{\sqrt{3}}\right) = \frac{\pi}{3},$$​​

since

​$$\cot\left(\frac{\pi}{3}\right) = \frac{1}{\sqrt{3}}$$​​

For negative arguments, we use:

​$$\cot^{-1}(-x) = \pi - \cot^{-1}(x)$$​​

Solution:

​$$\cot^{-1}\left(-\frac{1}{\sqrt{3}}\right) = \pi - \frac{\pi}{3} = \frac{2\pi}{3}$$​​