$\frac{1-\tan ^{2} 45^{\circ}}{1+\tan ^{2} 45^{\circ}}=$

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

$(\operatorname{cosec} A-\sin A)(\sec A-\cos A)=\frac{1}{\tan A+\cot A}$

Evaluate:

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

Write all the other trigonometric ratios of $\angle A$ in terms of $\sec$ $A$.

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

$(\operatorname{cosec} \theta-\cot \theta)^{2}=\frac{1-\cos \theta}{1+\cos \theta}$

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

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