$\sec^{-1}[\sec(-30^o)] = $ ....... $^o$

If ${\sin ^{ - 1}}\frac{1}{2} = {\tan ^{ - 1}}x,$ then $x =$

If $y = \sin^{-1}\left(\frac{2^{x+1}}{1+4^x}\right)$ and $\frac{dy}{dx} = \frac{2^{x+1} \log 2}{f(x)}$,then $f(0) = $ . . . . . .

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

$\tan ^{-1}\left(\frac{1+\sqrt{3}}{3+\sqrt{3}}\right)+\sec ^{-1}\left(\sqrt{\frac{8+4 \sqrt{3}}{6+3 \sqrt{3}}}\right)$ is equal to $.........$

Find the value of $\sin ^{-1}\left(\sin \frac{3 \pi}{5}\right)$