Answer
$ =\frac{4}{5}$
Work Step by Step
To find $\cos (\tan ^ {–1} \frac{3}{4})$
let, $\tan ^ {–1} \frac{3}{4} = \theta$
then, $\tan \theta = \frac{3}{4}$
We know, if
$\tan \theta = \frac{p}{b}$, then
$\cos \theta = \frac{b}{\sqrt{p^2 + b^2}}$
$\cos \theta = \frac{4}{\sqrt{3^2 + 4^2}}$
$ =\frac{4}{5}$
