$\frac{1-\tan ^{2} 45^{\circ}}{1+\tan ^{2} 45^{\circ}}=$
$\tan 90^{\circ}$
$1$
$0$
$\sin 45^{\circ}$
Prove the following identities, where the angles involved are acute angles for which the expressions are defined.
$\frac{\cos A}{1+\sin A}+\frac{1+\sin A}{\cos A}=2 \sec A$
Given $\tan A=\frac{4}{3},$ find the other trigonometric ratios of the $\angle A$
State whether the following are true or false. Justify your answer.
$(i)$ The value of tan $A$ is always less than $1 .$
$(ii)$ $\sec A=\frac{12}{5}$ for some value of angle $A$.
If $3 \cot A=4,$ check whether $\frac{1-\tan ^{2} A}{1+\tan ^{2} A}=\cos ^{2} A-\sin ^{2} A$ or not.
Evaluate:
$\frac{\sin 18^{\circ}}{\cos 72^{\circ}}$