If $\cot ^{-1}(\sqrt{\cos \alpha})-\tan ^{-1}(\sqrt{\cos \alpha})=x$, then the value of $\sin x$ is

Considering only the principal values of the inverse trigonometric functions, the value of $\tan \left(\sin ^{-1}\left(\frac{3}{5}\right)-2 \cos ^{-1}\left(\frac{2}{\sqrt{5}}\right)\right)$ is

If the area bounded by the curve $x^2=4 y, \mathrm{X}$-axis and the line $x=4$ is divided into equal areas by the line $x=\alpha$, then the value of $\alpha$ is …

If $p^3=q^4=r^6=t^7=s^2$, then $\log _t(p q r s)=\ldots \ldots$