If ${\cos }^{-1}\left(\cos 10\right)$ is equal to $a\pi +b$  then  $a-b=$ _____

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

Here  $\theta =10$ , rad, clearly, it does not lie between 0 and $\pi$  . 

But  $4\pi -10$  lies between 0 and  $\pi$  .

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