Find the Principal Value of cot-1(√3)
Solution:
Let
\[ y = \cot^{-1}(\sqrt{3}) \]
Then,
\[ \cot y = \sqrt{3} \]
We know:
\[ \cot\left(\frac{\pi}{6}\right) = \sqrt{3} \]
Principal value range of cot⁻¹(x):
\[ (0, \pi) \]
Since \( \frac{\pi}{6} \in (0,\pi) \),
\[ y = \frac{\pi}{6} \]
Final Answer:
Principal Value = \[ \frac{\pi}{6} \]