The solution of the inequality $\log_{1/2} \sin^{-1}x>\log_{1/2}\cos^{-1}x$ is:

$x∈[0,\frac{1}{\sqrt{2}}]$ $x∈(\frac{1}{\sqrt{2}},1]$ $x∈[0,\frac{1}{\sqrt{2}})$ None of these

None of these

$\sin^{-1}x<\cos^{-1}x;\sin^{-1}x<\frac{π}{2}-\sin^{-1}x$ $⇒\sin^{-1}x<\frac{π}{4}⇒0<x<\frac{1}{\sqrt{2}}$; Also, $\sin^{-1}x>0$