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MHT CET202616 April 2026Evening ShiftMathematicsInverse Trigonometric FunctionsActual

The value of ⁻¹ [ 1 - x + 1 + x 1 - x - 1 + x ] , where x (0, 2 ) is...

Options

  1. A- x
  2. B2 - x
  3. C2 - x 2
  4. D- x 2

Correct answer

D. - x 2

Step-by-step solution

We know that 1 x = ( x 2 x 2 )^2 . Since x (0, 2 ) , we have x 2 (0, 4 ) . In this interval, x 2 > x 2 > 0 . Therefore, 1 - x = x 2 - x 2 and 1 + x = x 2 + x 2 . Substituting these values into the given expression: 1 - x + 1 + x 1 - x - 1 + x = ( x 2 - x 2 ) + ( x 2 + x 2 ) ( x 2 - x 2 ) - ( x 2 + x 2 ) = 2 x 2 -2 x 2 = - x 2 The given expression becomes ⁻¹ (- x 2 ) . Using the property ⁻¹(-y) = - ⁻¹y : ⁻¹ (- x 2 ) = - ⁻¹ ( x 2 ) Since x 2 (0, 4 ) , ⁻¹ ( x 2 ) = x 2 . Thus, the value is - x 2 . Answer: - x 2

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