Evaluate the following:
$\sin 60^{\circ} \cos 30^{\circ} + \sin 30^{\circ} \cos 60^{\circ}$

Prove the following identity,where the angles involved are acute angles for which the expressions are defined:
$\frac{\tan \theta}{1-\cot \theta}+\frac{\cot \theta}{1-\tan \theta}=1+\sec \theta \operatorname{cosec} \theta$

State whether the following is true or false. Justify your answer.
The value of $\sin \theta$ increases as $\theta$ increases.

Prove the following identity,where the angles involved are acute angles for which the expressions are defined:
$\frac{\sin \theta - 2 \sin^3 \theta}{2 \cos^3 \theta - \cos \theta} = \tan \theta$

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

If $\angle B$ and $\angle Q$ are acute angles such that $\sin B = \sin Q$,then prove that $\angle B = \angle Q$.