Q. If in a $\mathrm{\Delta}\ ABC,\angle A = \tan^{- 1}{2\ and\ \angle B = \tan^{- 1}{3,}}\$then angle $C$ is equal to

A) $\frac{\pi}{2}$
B) $\frac{\pi}{3}$
C) $\frac{\pi}{4}$
D) None of these
Explanation

(c)
Given that, $\angle A = \tan^{- 1}{2,\angle B = \tan^{- 1}3}$
We know that, $\angle A + \angle B + \angle C = \pi$
$\Rightarrow \tan^{- 1}{2 + \tan^{- 1}{3 + \angle C = \pi}}$
$\Rightarrow \tan^{- 1}{\left( \frac{2 + 3}{1 - 2 \times 3} \right) + \angle C = \pi}$
$\Rightarrow \tan^{- 1}{( - 1) + \angle C = \pi}$
$\Rightarrow \frac{3\pi}{4} + \angle C = \pi$
$\Rightarrow \angle C = \frac{\pi}{4}$

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.