Question
Find the principal value of:
\[ \tan^{-1}(\sqrt{3}) + \cot^{-1}(\sqrt{3}) \]
Solution
Using standard values:
\[ \tan^{-1}(\sqrt{3}) = \frac{\pi}{3} \]
Also,
\[ \cot^{-1}(\sqrt{3}) = \frac{\pi}{6} \]
(since \( \cot \frac{\pi}{6} = \sqrt{3} \))
Therefore,
\[ \frac{\pi}{3} + \frac{\pi}{6} = \frac{\pi}{2} \]
Final Answer:
\[ \boxed{\frac{\pi}{2}} \]
Key Concept
Use standard inverse trigonometric values carefully within principal ranges.