MHT CET202526 Apr 2025Morning ShiftMathematicsInverse Trigonometric FunctionsActual
If ⁻¹(4 x)+ ⁻¹(4 3 x)=- 2 , then the absolute value of x is
Options
- A1 8
- B1 6
- C2 3
- D1 4
Correct answer
A. 1 8
Step-by-step solution
Given the equation ⁻¹(4x) + ⁻¹(4 3 x) = - 2 , begin by isolating one inverse sine term: ⁻¹(4x) = - 2 - ⁻¹(4 3 x) Apply the sine function to both sides: 4x = (- ( 2 + ⁻¹(4 3 x) ) ) Using trigonometric identities (- ) = - and ( 2 + ) = : 4x = - ( ⁻¹(4 3 x)) Since ( ⁻¹y) = 1-y^2 : 4x = - 1-(4 3 x)^2 The right side is negative, requiring x 16x^2 = 1 - (4 3 x)^2 16x^2 = 1 - 48x^2 64x^2 = 1 x^2 = 1 64 Thus x = 1 8 , but only x = - 1 8 satisfies x Verification confirms ⁻¹(- 1 2 ) + ⁻¹(- 3 2 ) = - 6 - 3 = - 2 . The absolut