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

Evaluate:
$\frac{\tan 26^{\circ}}{\cot 64^{\circ}}$

If $\sin 3A = \cos(A - 26^{\circ})$,where $3A$ is an acute angle,find the value of $A$.

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

Prove the following identity,where the angles involved are acute angles for which the expressions are defined:
$\frac{\cos A}{1+\sin A}+\frac{1+\sin A}{\cos A}=2 \sec A$

State whether the following is true or false. Justify your answer.
$\cot A$ is not defined for $A = 0^{\circ}$.