If the principal value of ${cosec}^{-1}\sqrt{2}$ is $\frac{\pi }{k}$, find the value of $\frac{k}{2}$.

The principal value of: ${\cos }^{-1}\left(-\frac{\sqrt{3}}{2}\right)$ is $\frac{m\pi }{6}$then $m=$

Principal value of ${\tan }^{-1}\left(\sqrt{3}\right)=m°$, $m=$

Principal value of ${cosec}^{-1}(-\sqrt{2})=k°$, $k=$

Evaluate $\cos \left\{{\cos }^{-1}\left(\frac{-\sqrt{3}}{2}\right)+\frac{\pi }{6}\right\}$.

Evaluate $\sin \left\{\frac{\pi }{2}-\left(\frac{-\pi }{3}\right)\right\}$