Evaluate:

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

In $\triangle$ $OPQ$, right-angled at $P$, $OP =7\, cm$ and $OQ - PQ =1\, cm$ (see $Fig.$). Determine the values of $\sin Q$ and $\cos Q$.

$(1+\tan \theta+\sec \theta)(1+\cot \theta-\operatorname{cosec} \theta)=..........$

Prove the following identities, where the angles involved are acute angles for which the expressions are defined.

$\sqrt{\frac{1+\sin A }{1-\sin A }}=\sec A +\tan A$

If $\tan A =\cot B ,$ prove that $A + B =90^{\circ}$

Evaluate the following:

$\frac{\sin 30^{\circ}+\tan 45^{\circ}-\operatorname{cosec} 60^{\circ}}{\sec 30^{\circ}+\cos 60^{\circ}+\cot 45^{\circ}}$