If [sin−1x]>[cos−1x] , where [.] denotes the greatest integer function, then complete set of values of x  is

[sin−1x]>[cos−1x] , 0≤cos−1x≤π ⇒  cos−1x=0,1,2 or 3  and −π/2≤sin−1x≤π/2 ⇒ sin−1x=−2,−1,0,1 [sin−1x]>[cos−1x] ⇒ [sin−1x]=1.[cos−1x]=0 ⇒ sin1≤x≤1 , cos1π/4, sin1>cos1 Hence, required set of values of x  is [sin1,1] .