Question

If the value of expression $\sin ^{-1}\left(\sin 2013^{\circ}\right)+\cos ^{-1}(\cos$ $\left.2013^{\circ}\right)+\tan ^{-1}\left(\tan 2013^{\circ}\right)$ is equal to $\left(k^{\circ}\right)$ where $k \in N$ then find the value of $\sqrt{\frac{k}{3}}$.

Answer 1

$\sin ^{-1}\left(\sin 2013^{\circ}\right)+\cos ^{-1}\left(\cos 2013^{\circ}\right)+\tan ^{-1}\left(\tan 2013^{\circ}\right)$
$=-\sin ^{-1} \sin 33^{\circ}+\pi-\cos ^{-1} \cos 33^{\circ}+\tan ^{-1} \tan 33^{\circ}$
$=\pi-33^{\circ}=147^{\circ}=k^{\circ}$
$\therefore $ The value of $\sqrt{\frac{k}{3}}=7$