If $\left[{\sin }^{-1}x\right]>\left[{\cos }^{-1}x\right]$ , where [.] denotes the greatest integer function, then complete set of values of $x$  is

$\left[{\sin }^{-1}x\right]>\left[{\cos }^{-1}x\right]$ , $0\le {\cos }^{-1}x\le \pi$

$\Rightarrow {\cos }^{-1}x=0,1,2or3$  and $-\pi /2\le {\sin }^{-1}x\le \pi /2\Rightarrow {\sin }^{-1}x=-2,-1,0,1$

$\left[{\sin }^{-1}x\right]>\left[{\cos }^{-1}x\right]$ $\Rightarrow \left[{\sin }^{-1}x\right]=1.\left[{\cos }^{-1}x\right]=0$

$\Rightarrow \sin 1\le x\le 1$ , $\cos 1<x\le 1$

Since $1>\pi /4,\sin 1>\cos 1$

Hence, required set of values of $x$  is $[\sin 1,1]$ .