Question

If $A+B+C=\pi$ and A,B,C are all greater then 0 and angle C is obtuse then

• A. $\tan A\tan B\ge 1$
• B. $\tan A\tan B<1$
• C. $\tan A\tan B=1$
• D. None of these

Answer 1

The correct option is B $\tan A\tan B<1$

$A+B=\pi -C$
$\Rightarrow \tan (A+B)=\tan (\pi -C)=-\tan C$
$\Rightarrow \frac{\tan A+\tan B}{1-\tan A\tan B}>0$ now $\tan A>0$
$\Rightarrow 1-\tan A\tan B>0$
or $\tan A\tan B<1$