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  • The principal value of the given equation   <img alt="y=tan^{-1}\left ( \frac{1}{\sqrt{3}} \right )" src="https://entrancecorner.oncodecogs.com/gif.latex?y%3Dtan%5E%7B-1%7D%5Cleft%20

The principal value of the given equation   y=tan^{-1}\left ( \frac{1}{\sqrt{3}} \right )   is

Option: 1

\frac{\pi}{4}


Option: 2

\frac{\pi}{3}


Option: 3

\frac{\pi}{2}


Option: 4

\frac{\pi}{6}


Answers (1)

best_answer

Given that,

 y=tan^{-1}\left ( \frac{1}{\sqrt{3}} \right )

tan\ y=\left ( \frac{1}{\sqrt{3}} \right )

We know that the range of the principal value branch of  tan^{-1}x  is  \left ( -\frac{\pi}{2},\frac{\pi}{2} \right ).

Thus,

 tan\left ( \frac{\pi}{6} \right )=\frac{1}{\sqrt{3}}

Therefore, the principal value of  tan^{-1}\left ( \frac{1}{\sqrt{3}} \right )=\frac{\pi}{6}.


 

Posted by

Anam Khan

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