Evaluate:
$\frac{\sin 18^{\circ}}{\cos 72^{\circ}}$

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

Show that:
$(i)$ $\tan 48^{\circ} \tan 23^{\circ} \tan 42^{\circ} \tan 67^{\circ} = 1$
$(ii)$ $\cos 38^{\circ} \cos 52^{\circ} - \sin 38^{\circ} \sin 52^{\circ} = 0$

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.

Express $\cot 85^{\circ}+\cos 75^{\circ}$ in terms of trigonometric ratios of angles between $0^{\circ}$ and $45^{\circ}$.