jmc

Since $△XYZ$ is a right triangle with $\angle X=90^{\circ }$, we have $\tan Z=\frac{XY}{XZ}$. Since $\tan Z=3$, we have $XY=3k$ and $XZ=k$ for some value of $k$, as shown in the diagram. Applying the Pythagorean Theorem gives $Y{Z}^2=(3k{)}^2+k^2=10k^2$, so $YZ=k\sqrt{10}$.

Finally, we have $\cos Z=\frac{XZ}{YZ}=\frac{k}{k\sqrt{10}}=\frac{1}{\sqrt{10}}=\boxed{\frac{\sqrt{10}}{10}}$.