Evaluate:
$\frac{\sin 18^{\circ}}{\cos 72^{\circ}}$
Evaluate the following:
$\sin 60^{\circ} \cos 30^{\circ}+\sin 30^{\circ} \cos 60^{\circ}$
Write all the other trigonometric ratios of $\angle A$ in terms of $\sec$ $A$.
If $\cot \theta=\frac{7}{8},$ evaluate:
$(i)$ $\frac{(1+\sin \theta)(1-\sin \theta)}{(1+\cos \theta)(1-\cos \theta)}$
$(ii)$ $\cot ^{2} \theta$
Prove the following identities, where the angles involved are acute angles for which the expressions are defined.
$\sqrt{\frac{1+\sin A }{1-\sin A }}=\sec A +\tan A$