Write 'True' or 'False' and justify your answer.
$\tan \theta$ increases faster than $\sin \theta$ as $\theta$ increases for $0^\circ < \theta < 90^\circ$.

(A) True.
We know that $\sin \theta$ increases as $\theta$ increases,but $\cos \theta$ decreases as $\theta$ increases in the interval $0^\circ < \theta < 90^\circ$.
We have $\tan \theta = \frac{\sin \theta}{\cos \theta}$.
As $\theta$ increases from $0^\circ$ to $90^\circ$,$\sin \theta$ increases (numerator increases) and $\cos \theta$ decreases (denominator decreases).
Since $\tan \theta$ is the ratio of an increasing value to a decreasing value,it grows at a significantly faster rate compared to $\sin \theta$,which is simply the ratio of an increasing value to a constant value of $1$.
Therefore,$\tan \theta$ increases faster than $\sin \theta$ as $\theta$ increases.