Q. If $A + B = \frac{\pi}{4}$, then $\left( \tan{A + 1} \right)(\tan{B + 1})$ equals
A) 1
B) $\sqrt{3}$
C) 2
D) $\frac{1}{\sqrt{3}}$
Explanation
(c)
$A + B = \frac{\pi}{4}\ \ \ \Rightarrow \ \tan{(A + B) = 1}$
$\Rightarrow \frac{\tan{A + \tan B}}{1 - \tan{A\tan B}} = 1$
$\Rightarrow \ \tan{A + \tan{B + \tan{A\tan{B = 1}}}}$
$\Rightarrow \ \ \ \left( 1 + \tan A \right)\left( 1 + \tan B \right) = 1 + 1 = 2$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.