The value of $\sin \left(2 \sin ^{-1} 0.8\right)$ is equal to

The value of $\sec ^{-1}\left(\frac{1}{4} \sum_{k=0}^{10} \sec \left(\frac{7 \pi}{12}+\frac{k \pi}{2}\right) \sec \left(\frac{7 \pi}{12}+\frac{(k+1) \pi}{2}\right)\right)$ in the interval $\left[-\frac{\pi}{4}, \frac{3 \pi}{4}\right]$ equals

The principal value of ${\sin ^{ - 1}}\left( { - \frac{{\sqrt 3 }}{2}} \right)$ is

The value of $\cos ^{-1}\left(\cos \left(\frac{7 \pi}{6}\right)\right)$ is

If $f(x) = \sin^{-1}(\sin x)$; $x \in R$,then $f$ is

Find the principal value of $cosec^{-1}(2)$.