Evaluate:
$\cos 48^{\circ}-\sin 42^{\circ}$

In $\triangle PQR$, right-angled at $Q$, $PR + QR = 25 \, cm$ and $PQ = 5 \, cm$. Determine the values of $\sin P, \cos P$ and $\tan P$.

In $\triangle PQR$,right-angled at $Q$,$PQ = 3 \, cm$ and $PR = 6 \, cm$. Determine $\angle QPR$ and $\angle PRQ$.

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

Evaluate the following:
$\frac{\sin 30^{\circ}+\tan 45^{\circ}-\operatorname{cosec} 60^{\circ}}{\sec 30^{\circ}+\cos 60^{\circ}+\cot 45^{\circ}}$

Prove the following identity,where the angles involved are acute angles for which the expressions are defined:
$\frac{\sin \theta - 2 \sin^3 \theta}{2 \cos^3 \theta - \cos \theta} = \tan \theta$