Question

The value of \( \tan^{-1}(1) + \tan^{-1}(2) + \tan^{-1}(3) \) is:

• A. $\pi$
• B. $\pi/2$
• C. $0$
• D. $\pi/4$

Hint:

This is a standard result in inverse trigonometry.

Answer 1

The Correct Option is A

Step 1: Concept
Use the identity $\tan^{-1}x + \tan^{-1}y = \pi + \tan^{-1}\left(\frac{x+y}{1-xy}\right)$ if $xy>1$.
Step 2: Analysis
$\tan^{-1}(2) + \tan^{-1}(3) = \pi + \tan^{-1}\left(\frac{2+3}{1-6}\right) = \pi + \tan^{-1}(-1) = \pi - \pi/4$. Now, add $\tan^{-1}(1)$: $(\pi - \pi/4) + \pi/4$.
Step 3: Conclusion
Result $= \pi$.
Final Answer: (A)