Mark the tick against the correct answer in the following:
$\cos \left(\tan ^{-1} \frac{3}{4}\right)=?$
A. $\frac{3}{5}$
B. $\frac{4}{5}$
C. $\frac{4}{9}$
D. none of these
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, $\cos \left(\tan ^{-1} \frac{3}{4}\right)=\cos x=\frac{4}{5}$
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