Evaluate:
$\frac{\sin ^{2} 63^{\circ}+\sin ^{2} 27^{\circ}}{\cos ^{2} 17^{\circ}+\cos ^{2} 73^{\circ}}$

Express the trigonometric ratios $\sin A$,$\sec A$,and $\tan A$ in terms of $\cot A$.

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 $\cos \theta$ increases as $\theta$ increases.

$9 \sec^{2} A - 9 \tan^{2} A = \dots$

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