Question

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

Answer 1

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

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

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

$={10}^{\circ }-(-{10}^{\circ })={20}^{\circ }$
$\therefore {\cos }^{-1}\left(\cos {350}^{\circ }\right)-{\sin }^{-1}\left(\sin {350}^{\circ }\right)={20}^{\circ }$