State whether the following is true or false. Justify your answer.
The value of $\sin \theta$ increases as $\theta$ increases.

State whether the following is true or false. Justify your answer.
The value of $\cos \theta$ increases as $\theta$ increases.

Given $\tan A = \frac{4}{3},$ find the other trigonometric ratios of the $\angle A$.

Prove the following identity,where the angles involved are acute angles for which the expressions are defined:
$(\operatorname{cosec} \theta - \cot \theta)^2 = \frac{1 - \cos \theta}{1 + \cos \theta}$

If $3 \cot A = 4$,check whether $\frac{1 - \tan^2 A}{1 + \tan^2 A} = \cos^2 A - \sin^2 A$ or not.

In $\triangle ABC$,right-angled at $B$,$AB = 24 \, cm$,$BC = 7 \, cm$. Determine:
$(i)$ $\sin A, \cos A$
$(ii)$ $\sin C, \cos C$