Write the value

Question:

Write the value of $\cos ^{-1}\left(\cos 350^{\circ}\right)-\sin ^{-1}\left(\sin 350^{\circ}\right)$

Solution:

We have

$\cos ^{-1}\left(\cos 350^{\circ}\right)-\sin ^{-1}\left(\sin 350^{\circ}\right)$

$=\cos ^{-1}\left\{\cos \left(360^{\circ}-350^{\circ}\right)\right\}-\sin ^{-1}\left\{\sin \left(360^{\circ}-350^{\circ}\right)\right\}$                    $\left[\because \sin \left(360^{\circ}-x\right)=-\sin x, \quad \cos \left(360^{\circ}-x\right)=\cos x\right]$

$=\cos ^{-1}\left\{\cos \left(10^{\circ}\right)\right\}-\sin ^{-1}\left\{\sin \left(-10^{\circ}\right)\right\}$

$=10^{\circ}-\left(-10^{\circ}\right)$

$=20^{\circ}$

$\therefore \cos ^{-1}\left(\cos 350^{\circ}\right)-\sin ^{-1}\left(\sin 350^{\circ}\right)=20^{\circ}$

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