Evaluate $\frac{\tan 65^{\circ}}{\cot 25^{\circ}}$

In $\triangle OPQ$,right-angled at $P$,$OP = 7\, cm$ and $OQ - PQ = 1\, cm$. Determine the values of $\sin Q$ and $\cos Q$.

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

Prove the following identity,where the angles involved are acute angles for which the expressions are defined:
$\frac{\cos A}{1+\sin A}+\frac{1+\sin A}{\cos A}=2 \sec A$

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

$9 \sec^{2} A - 9 \tan^{2} A = \dots$