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

$\sin (2{\sin ^{ - 1}}0.8) = $

$A$ value of $x$ for which $\sin(\cot^{-1}(1 + x)) = \cos(\tan^{-1}x)$ is

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

Find the value of $\tan ^{-1}\left(\tan \frac{7 \pi}{6}\right)$

If $y = \tan^{-1} \left[ \frac{x - \sqrt{1 - x^2}}{x + \sqrt{1 - x^2}} \right]$, then $\frac{dy}{dx} =$