Q. The value of $\tan^{- 1}{(1) + \tan^{- 1}{(0) + \tan^{- 1}{(2) + \tan^{- 1}{(3)}}}}\$is equal to
A) $\pi$
B) $\frac{5\pi}{4}$
C) $\frac{\pi}{2}$
D) None of these
Explanation
(a)
$\tan^{- 1}{(1) + \tan^{- 1}{(0) + \tan^{- 1}{(2) + \tan^{- 1}{(3)}}}}$
$= \frac{\pi}{4} + \pi + \tan^{- 1}\left( \frac{2 + 3}{1 - 2 \bullet 3} \right)$ (as 2$\bullet$3>1)
$= \frac{5\pi}{4} + \tan^{- 1}{( - 1) = \frac{5\pi}{4} - \frac{\pi}{4} = \pi}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.