The value of ${\cos }^{-1}(\cos 10)$, is

We know that ${\cos }^{-1}(\cos \theta )=\theta ,\text{ if }0\le \theta \le \pi$

Here, $\theta =10$ radians

Clearly, it does not lie between O and $\mathrm{\pi }$ However ($4\mathrm{\pi }-10$) between O and $\mathrm{\pi }$ such that cos ($4\mathrm{\pi }-10$)=cos 10

$\therefore {\cos }^{-1}(\cos 10)={\cos }^{-1}(\cos (4\pi -10\left)\right)=4\pi -10$