The value of cos^-1 (cos 10), is

We know that $cos^{-1} (cos θ)= θ$ if $0 ≤ θ ≤ \pi $.

Here, $θ = 10$ radians.

Clearly, it does not lie between 0 and $\pi $. However, $(4\pi - 10)$ lies between 0 and $\pi $ such that $cos (4\pi - 10)$ = cos 10.

∴ $cos^{-1}(cos10)= cos^{-1}(cos(4\pi - 10)) = 4 \pi - 10 $