$\sin 2 A=2 \sin A$ is true when $A=$

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 $AC .$

If $\sin A =\frac{3}{4},$ calculate $\cos A$ and $\tan A$.

In $Fig.$ find $\tan P-\cot R .$

In $\triangle$ $PQR,$ right-angled at $Q$ (see $Fig.$), $PQ =3 \,cm$ and $PR =6 \,cm$. Determine $\angle QPR$ and $\angle PRQ$.

Evaluate the following:

$\sin 60^{\circ} \cos 30^{\circ}+\sin 30^{\circ} \cos 60^{\circ}$