Explanation

(a)
Since, angle $C$ is obtuse, angle $A$ and $B$ are actute
$\therefore\tan{C < 0}$and${\ tan}{A > 0,\tan{B > 0}}$
Now, $\tan{(A + B) = \frac{\tan{A + \tan B}}{1 - \tan{A\ \tan B}}}$
$\Rightarrow \tan{(\pi - C) = \frac{\tan{A + \tan B}}{1 - \tan{A\ tan\ B}}}$
$\Rightarrow - \tan{C = \frac{\tan{A + \tan B}}{1 - \tan{A\tan B}}}$
$\Rightarrow 1 - \tan{A\tan{B > 0\ \ \ (\because}}\$Numerator are positive)
$\Rightarrow \tan{A\tan{B < 1}}$