If $y = \sin^{-1}\left(\frac{19}{20}x\right) + \cos^{-1}\left(\frac{19}{20}x\right)$,then $\frac{dy}{dx} = $

If $\cos ^{-1} \alpha+\cos ^{-1} \beta+\cos ^{-1} \gamma=3 \pi$, then $\alpha(\beta+\gamma)+\beta(\gamma+\alpha)+\gamma(\alpha+\beta)$ is equal to

Let $x \in (0, 1)$. The set of all $x$ such that $\sin^{-1} x > \cos^{-1} x$ is the interval

$\sin ^{-1} \frac{\sqrt{3}}{2} + \sin ^{-1} \sqrt{\frac{2}{3}} = $

If $y = \tan^{-1} \left( \frac{x^{1/3} + a^{1/3}}{1 - x^{1/3}a^{1/3}} \right)$,then $\frac{dy}{dx} = $

If $2 \sin^{-1} x = \sin^{-1}(2x \sqrt{1-x^2})$,then $x \in$ . . . . . . .