logo

Ask Questions, Get Answers

 
X
 Search
Want to ask us a question? Click here
Browse Questions
Ad
0 votes

The principal value of $ \tan^{-1}\sqrt 3 $ is _______________.

$\begin{array}{1 1} \frac{\pi}{6} \\ \frac{-\pi}{6} \\ \frac{\pi}{3} \\ \frac{-\pi}{3} \end{array} $

Can you answer this question?
 
 

1 Answer

0 votes
Toolbox:
  • The range of the principal value of $\; tan^{-1}x$ is $\left (- \large\frac{\pi}{2},\large\frac{\pi}{2} \right )$
Ans : \( tan^{-1}tan\large\frac{\pi}{3}=\large\frac{\pi}{3} \)
 
Let $tan^{-1}\sqrt 3 = x \Rightarrow tan (x) = \sqrt 3$
 
We know that the range of the principal value of $\; tan^{-1}x$ is $\left (- \large\frac{\pi}{2},\large\frac{\pi}{2} \right)$
\( \therefore\) $tan(x) = \sqrt 3 = tan \large\frac{\pi}{3}$
 
$\Rightarrow x=\large\frac{\pi}{3}$, where\( x\:\in\: \left (- \large\frac{\pi}{2},\large\frac{\pi}{2} \right )\)
Therefore, the principal value of $tan^{-1}(\sqrt 3) is \large\frac{\pi}{3}$

 

answered Feb 18, 2013 by thanvigandhi_1
edited Mar 16, 2013 by thanvigandhi_1
 
Ask Question
student study plans
x
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App
...