Answer
$\frac{40}{41}$
Work Step by Step
Given the ratio of $\frac{9}{40}$, we can draw a right triangle as shown in the figure.
For angle $t$, we have $tan(t)=\frac{9}{40}$ and $t=tan^{-1}\frac{9}{40}$
The hypotenuse $x$ can be found as $x=\sqrt {40^2+9^2}=41$ and $cos(t)=\frac{40}{41}$
Thus $cos(tan^{-1}\frac{9}{40})=cos(t)=\frac{40}{41}$
