Answer
$=\frac{5}{3}$
Work Step by Step
$\csc (\tan ^ {–1} \frac{3}{4})$
let, $\tan ^ {–1} \frac{3}{4} = \theta$
then, $\tan \theta =\frac{3}{4}$
We know, $\csc \theta = \sqrt{1+ \cot ^2 \theta}$
$\csc \theta = \sqrt{1 +( \frac{4}{3})^2}$
$ =\frac{5}{3}$