Question

If $A+B=\frac{\pi }{4}$ then $(1+\tan A)(1+\tan B)$ is equal to

• A. 1
• B. 2
• C. $\sqrt{3}$
• D. None of these

Answer 1

The correct option is B 2

$\tan (A+B)=\tan \pi /4=1$
$\Rightarrow \frac{\tan A+\tan B}{1-\tan A\tan B}=1$
$\Rightarrow \tan A+\tan B=1-\tan A\tan B$
$\Rightarrow 1+\tan A+\tan B+\tan A\tan B=2$
$\Rightarrow (1+\tan A)(1+\tan B)=2$