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Mark the tick against the correct answer in the following:

Question:

Mark the tick against the correct answer in the following:

The principal value of $\tan ^{-1}(-\sqrt{3})$ is

A. $\frac{2 \pi}{3}$

B. $\frac{4 \pi}{3}$

C. $\frac{-\pi}{3}$

D. none of these

Solution:

To Find: The Principle value of $\tan ^{-1}(-\sqrt{3})$

Let the principle value be given by $x$

Now, let $x=\tan ^{-1}(-\sqrt{3})$

$\Rightarrow \tan x=-\sqrt{3}$

$\Rightarrow \tan x=-\tan \left(\frac{\pi}{3}\right)\left(\because \tan \left(\frac{\pi}{3}\right)=-\sqrt{3}\right)$

$\Rightarrow \tan x=\tan \left(-\frac{\pi}{3}\right)(\because-\tan (\theta)=\tan (-\theta))$

$\Rightarrow x=-\frac{\pi}{3}$

 

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