Find the Principal Value of tan-1(1/√3)
Solution:
Let
\[ y = \tan^{-1}\left(\frac{1}{\sqrt{3}}\right) \]
Then,
\[ \tan y = \frac{1}{\sqrt{3}} \]
We know that:
\[ \tan\left(\frac{\pi}{6}\right) = \frac{1}{\sqrt{3}} \]
Since the principal value range of tan-1(x) is:
\[ \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \]
Therefore,
\[ y = \frac{\pi}{6} \]
Final Answer:
Principal Value = \[ \frac{\pi}{6} \]