Evaluate:
$\cos 48^{\circ}-\sin 42^{\circ}$
Prove the following identities, where the angles involved are acute angles for which the expressions are defined.
$\left(\frac{1+\tan ^{2} A}{1+\cot ^{2} A}\right)=\left(\frac{1-\tan A}{1-\cot A}\right)^{2}=\tan ^{2} A$
Given $\tan A=\frac{4}{3},$ find the other trigonometric ratios of the $\angle A$
If $\sec 4 A =\operatorname{cosec}\left( A -20^{\circ}\right),$ where $4 A$ is an acute angle, find the value of $A$. (in $^{\circ}$)
If $\sin A =\frac{3}{4},$ calculate $\cos A$ and $\tan A$.