$\frac{2 \tan 30^{\circ}}{1-\tan ^{2} 30^{\circ}} = ?$

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

$\sin 2A = 2 \sin A$ is true when $A =$ (in $^{\circ}$)

State whether the following are true or false. Justify your answer.
$(i)$ The value of $\tan A$ is always less than $1$.
$(ii)$ $\sec A = \frac{12}{5}$ for some value of angle $A$.

If $A, B$ and $C$ are interior angles of a triangle $ABC$,then show that $\sin \left(\frac{B+C}{2}\right) = \cos \frac{A}{2}$.

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