MHT CET202526 Apr 2025Evening ShiftMathematicsInverse Trigonometric FunctionsActual
If ⁻¹( )- ⁻¹( )=x , then the value of x is
Options
- A^2 2
- B2
- C2
- D^2 2
Correct answer
D. ^2 2
Step-by-step solution
Given the expression x = ⁻¹ ( 1 ( 2 ) ) - ⁻¹ ( ( 2 ) ) . Using the identity ⁻¹(y) + ⁻¹ ( 1 y ) = 2 for y > 0 where y = ( 2 ) , we have: ⁻¹ ( 1 ( 2 ) ) = 2 - ⁻¹ ( ( 2 ) ) Substituting into the expression for x : x = ( 2 - ⁻¹ ( ( 2 ) ) ) - ⁻¹ ( ( 2 ) ) x = 2 - 2 ⁻¹ ( ( 2 ) ) Considering the given alternative form ⁻¹( ) - ⁻¹( ) = x Using ⁻¹ y = 2 - ⁻¹ y : x = ( 2 - ⁻¹( ) ) - ⁻¹( ) x = 2 - 2 ⁻¹( ) To find x : x = ( 2 - 2 ⁻¹( ) ) Using ( 2 - ) = : x = (2 ⁻¹( ) ) Let y = and = ⁻¹(y) , so = y Using the identity (2 ) = 1 -