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MHT CET202618 April 2026Evening ShiftMathematicsInverse Trigonometric FunctionsActual

For x > 0 , if ( ⁻¹x + ⁻¹x) - ( ⁻¹x + ⁻¹x) = ( ⁻¹2) then x =

Options

  1. A1 2
  2. B1 2
  3. C3 2
  4. D1

Correct answer

B. 1 2

Step-by-step solution

Given equation: ( ⁻¹x + ⁻¹x) - ( ⁻¹x + ⁻¹x) = ( ⁻¹2) Let = ⁻¹x and = ⁻¹x . We know that ⁻¹x + ⁻¹x = 2 , so ⁻¹x = 2 - . The second term on the left hand side becomes ( 2 - + ) = ( - ) . The left hand side simplifies to ( + ) - ( - ) = 2 . Since = ⁻¹x , we have = x . Since = ⁻¹x , we have = x 1+x^2 . Thus, the left hand side is 2x ( x 1+x^2 ) = 2x^2 1+x^2 . For the right hand side, let = ⁻¹2 , then = 2 , which gives = 1 1+ ^2 = 1 5 . Equating both sides: 2x^2 1+x^2 = 1 5 Squaring both sides: 4x^4 1+x^2 = 1 5 20x^4 =

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