$\frac{2 \tan 30^{\circ}}{1-\tan ^{2} 30^{\circ}}=$
$\tan 60^{\circ}$
$\cos 60^{\circ}$
$\sin 60^{\circ}$
$\sin 30^{\circ}$
Given $\tan A=\frac{4}{3},$ find the other trigonometric ratios of the $\angle A$
Evaluate:
$\operatorname{cosec} 31^{\circ}-\sec 59^{\circ}$
Prove the following identities, where the angles involved are acute angles for which the expressions are defined.
$\frac{1+\sec A}{\sec A}=\frac{\sin ^{2} A}{1-\cos A}$
In $\triangle$ $ABC,$ right-angled at $B$, $AB =5\, cm$ and $\angle ACB =30^{\circ}$ (see $Fig.$). Determine the lengths of the sides $BC$ and $AC .$
Express the ratios $\cos A ,$ tan $A$ and $\sec A$ in terms of $\sin A .$