${\mathrm{Cos}}^{-1}\left(\cos 12\right)-{\mathrm{Sin}}^{-1}\left(\sin 12\right)=$

$$\begin{gathered} 1^{\mathrm{c}}=57.2 \Rightarrow {12}^{\mathrm{c}}=686.4=4\mathrm{\pi }-33.6 \\ {\cos }^{-1}\left(\mathrm{as}\right(4\mathrm{\pi }-33.6\left)\right)=33.6 \\ {\sin }^{-1}\left(\sin \right(4\mathrm{\pi }-33.6\left)\right)=33.6 \\ {\cos }^{-1}(\mathrm{as} 12)-{\sin }^{-1}(\sin 12)=33.6+33.6 \\ =2(4\mathrm{\pi }-12)=8\mathrm{\pi }-24 \end{gathered}$$