If ( ⁻¹ x )^2- ( ⁻¹ x )^2>0 , then

Step-by-step solution

The inequality ( ⁻¹ x )^2 - ( ⁻¹ x )^2 > 0 factors as ( ⁻¹ x - ⁻¹ x)( ⁻¹ x + ⁻¹ x) > 0 . Using the identity ⁻¹ x + ⁻¹ x = 2 , the inequality simplifies to ( ⁻¹ x - ⁻¹ x) ( 2 ) > 0 . Since 2 > 0 , this reduces to ⁻¹ x > ⁻¹ x . Substituting ⁻¹ x = 2 - ⁻¹ x gives ⁻¹ x Taking sine of all terms, and noting (t) is increasing on [- 2 , 2 ] , yields -1 x This corresponds to option D .