Answer
$$\frac{1}{\sqrt 2}$$
Work Step by Step
Assume that $\cot\theta =\frac{1}{1}$, then by solving the triangle, we have:
$$\cos\theta=\frac{1}{\sqrt 2}.$$
Now, since $\theta =\cot^{-1}1 $, we have
$$\cos(\cot^{-1}1 )=\cos\theta=\frac{1}{\sqrt 2} .$$
