If [ si n − 1 x ] > [ co s − 1 x ] where [.] denotes greatest integer function, then the range of ‘ x ’ contains (also x > 0 )

Step-by-step solution

[ si n − 1 x ] = 0 , x ∈ ( 0 , s i n 1 ] = 1 , x ∈ [ s i n 1 , 1 ] [ co s − 1 x ] = 1 , x ∈ ( 0 , c o s 1 ] = 0 , x ∈ ( c o s 1 , 1 ] ∴ [ si n − 1 x ] > [ co s − 1 x ] ⇒ [ si n − 1 x ] = 1 , [ co s − 1 x ] = 0 ⇒ x ∈ [ s i n 1 , 1 ]