Answer
$\pi$
Work Step by Step
The range of $\cos^{-1}{x}$ is $[0, \pi]$.
Here, $\tan(\dfrac{-\pi}{4})=-1$, because $\cos(\pi)=-1$ and $\pi$ lies in the range of $\cos^{-1}{x}$ .
Therefore, we have:
$\cos^{-1}(\tan {(\dfrac{-\pi }{4})}]=\cos^{-1} (-1)=\pi$
