The value of  ${\sin }^{-1}\left(\sin 17\right)+{\cos }^{-1}\left(\cos 10\right)$ is equal to 
 

$\begin{array}{l}{\sin }^{-1}\left(\sin 17\right)={\sin }^{-1}\sin (17-5\pi +5\pi )=5\pi -17\\ {\cos }^{-1}\left(\cos 10\right)={\cos }^{-1}\cos (10-3\pi +3\pi )\\ ={\cos }^{-1}\cos \{3\pi +(10-3\pi )\}\\ ={\cos }^{-1}\{-\cos (10-3\pi )\}\\ =\pi -{\cos }^{-1}\cos \{10-3\pi \}\\ =\pi -(10-3\pi )=4\pi -10\end{array}$

Hence,  ${\sin }^{-1}\sin 17+{\cos }^{-1}\left(\cos 10\right)=9\pi -27$