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MHT CET202611 April 2026Evening ShiftMathematicsInverse Trigonometric FunctionsActual

If ( ⁻¹ x) = ( ⁻¹ a b^2 - a^2 ) , then the value of x is

Options

  1. Ab 2b^2 + a^2
  2. B2b^2 - a^2 b
  3. C2b^2 + a^2 b
  4. Db 2b^2 - a^2

Correct answer

D. b 2b^2 - a^2

Step-by-step solution

Let ⁻¹ x = = x = = x 1 - x^2 Let ⁻¹ a b^2 - a^2 = = a b^2 - a^2 = 1 + ^2 = 1 + a^2 b^2 - a^2 = b b^2 - a^2 Given = , we have: x 1 - x^2 = b b^2 - a^2 Squaring both sides: x^2 1 - x^2 = b^2 b^2 - a^2 x^2(b^2 - a^2) = b^2(1 - x^2) x^2 b^2 - x^2 a^2 = b^2 - x^2 b^2 x^2(2b^2 - a^2) = b^2 x^2 = b^2 2b^2 - a^2 x = b 2b^2 - a^2 Answer: b 2b^2 - a^2

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