Find the principal values of the following:

    4. \tan^{-1}(-\sqrt3)

Answers (1)

Let us assume that \tan^{-1}(-\sqrt3) = x, then we have;

\tan x = (-\sqrt 3) or

 -\tan (\frac{\pi}{3}) = \tan \left ( \frac{-\pi}{3} \right ).

and as we know that the principal value of \tan^{-1} is \left ( \frac{-\pi}{2}, \frac{\pi}{2} \right ).

Hence the only principal value of \tan^{-1}(-\sqrt3) when x = \frac{-\pi}{3}.

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