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AP EAMCET202423 May 2024Morning ShiftMathematicsInverse Trigonometric FunctionsActual

If 0 x 1 2 and = ⁻¹ x+ ⁻¹ ( x 2 + 3-3 x^2 2 ) , then + =

Options

  1. A4 3
  2. B4 3
  3. C4 x 1-x^2
  4. Dx 1-x^2

Correct answer

A. 4 3

Step-by-step solution

Given that aligned & = ⁻¹ x+ ⁻¹ ( x 2 + 3-3 x^2 2 ), 0 x 1 2 & = ⁻¹ x+ ⁻¹ ( 1 2 x+ 3 2 1-x^2 ) aligned Let x= aligned & = ⁻¹( )+ ⁻¹ ( 3 + 3 ) & = ⁻¹ ( ( 2 - ) )+ ⁻¹ ( ( - 3 ) ) & = 2 - + - 3 = 6 . aligned So, + = 6 + 6 = 1 3 + 3 = 4 3 .

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