Evaluate:

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

$\frac{2 \tan 30^{\circ}}{1+\tan ^{2} 30^{\circ}}=$

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

$\left(\frac{1+\tan ^{2} A}{1+\cot ^{2} A}\right)=\left(\frac{1-\tan A}{1-\cot A}\right)^{2}=\tan ^{2} A$

$\frac{2 \tan 30^{\circ}}{1-\tan ^{2} 30^{\circ}}=$

Evaluate:

$\sin 25^{\circ} \cos 65^{\circ}+\cos 25^{\circ} \sin 65^{\circ}$

State whether the following are true or false. Justify your answer.

$\cot$ $A$ is not defined for $A =0^{\circ}$