Write 'True' or 'False' and justify your answer.
The value of $\tan \theta$ (where $\theta < 90^{\circ}$) increases as $\theta$ increases.

(A) True.
In the figure,point $B$ is moved closer to $C$ along the line segment $BC$. It is observed that:
$(i)$ The angle $\theta$ increases (as $\theta_{1} > \theta, \theta_{2} > \theta_{1}, \dots$) and
(ii) The length of the base $BC$ decreases (as $B_{1}C < BC, B_{2}C < B_{1}C, \dots$)
In a right-angled triangle,$\tan \theta = \frac{\text{Perpendicular}}{\text{Base}} = \frac{AC}{BC}$.
Since the perpendicular $AC$ remains fixed and the base $BC$ decreases as $\theta$ increases,the ratio $\frac{AC}{BC}$ increases. Hence,$\tan \theta$ increases as $\theta$ increases.