$Co{s}^{-1}\left(\cos 12\right)-Si{n}^{-1}\left(\sin 12\right)=$

$$\begin{gathered} {\cos }^{-1}\left(\cos 12\right)=y\Rightarrow \cos y=\cos 12 \Rightarrow y=2n\pi +12,2n\pi -12 \\ Put n=2\Rightarrow y=4\pi -12 \Rightarrow {\sin }^{-1}\left(\sin 12\right)=z{\sin }^{-1}\left(\sin 12\right)=z \\ \Rightarrow \sin z=\sin 12\Rightarrow z=n\pi +{(-1)}^{n}12 Put n=-4\Rightarrow z=-4\pi +12 \end{gathered}$$