Mark the tick against the correct answer in the following:

To Find: The value of $\cos \left(\tan ^{-1} \frac{3}{4}\right)$

Let $x=\tan ^{-1} \frac{3}{4}$

$\Rightarrow \tan x=\frac{3}{4}$

$\Rightarrow \tan x=\frac{3}{4}=\frac{\text { oppositeside }}{\text { adjacent side }}$

We know that by pythagorus theorem ,

(Hypotenuse $)^{2}=$ (opposite side $)^{2}+(\text { adjacent side })^{2}$

Therefore, Hypotenuse = 5

$\Rightarrow \cos \mathrm{X}=\frac{\text { adjacent side }}{\text { hypotenuse }}=\frac{4}{5}$

Since here $x=\tan ^{-1} \frac{3}{4}$ hence $\cos \left(\tan ^{-1} \frac{3}{4}\right)$ becomes $\cos x$

Hence, $\cos \left(\tan ^{-1} \frac{3}{4}\right)=\cos x=\frac{4}{5}$