Question:
Write the value of $\cos ^{-1}\left(\cos 350^{\circ}\right)-\sin ^{-1}\left(\sin 350^{\circ}\right)$
Solution:
We have
$\cos ^{-1}\left(\cos 350^{\circ}\right)-\sin ^{-1}\left(\sin 350^{\circ}\right)$
$=\cos ^{-1}\left\{\cos \left(360^{\circ}-350^{\circ}\right)\right\}-\sin ^{-1}\left\{\sin \left(360^{\circ}-350^{\circ}\right)\right\}$ $\left[\because \sin \left(360^{\circ}-x\right)=-\sin x, \quad \cos \left(360^{\circ}-x\right)=\cos x\right]$
$=\cos ^{-1}\left\{\cos \left(10^{\circ}\right)\right\}-\sin ^{-1}\left\{\sin \left(-10^{\circ}\right)\right\}$
$=10^{\circ}-\left(-10^{\circ}\right)$
$=20^{\circ}$
$\therefore \cos ^{-1}\left(\cos 350^{\circ}\right)-\sin ^{-1}\left(\sin 350^{\circ}\right)=20^{\circ}$