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MHT CET20239 May 2023Evening ShiftMathematicsInverse Trigonometric FunctionsActual

The value of ⁻¹ ( 1+x^2 + 1-x^2 1+x^2 - 1-x^2 ) , |x| < 1 2 , x 0

Options

  1. A4 + 1 2 ⁻¹ x^2
  2. B4 + ⁻¹ x^2
  3. C4 - 1 2 ⁻¹ x^2
  4. D4 - ⁻¹ x^2

Correct answer

A. 4 + 1 2 ⁻¹ x^2

Step-by-step solution

Let T = ⁻¹ ( 1+x^2 + 1-x^2 1+x^2 - 1-x^2 ) Put x^2= 2 = 1 2 ⁻¹ x^2 aligned T & = ⁻¹ ( 1+ 2 + 1- 2 1+ 2 - 1- 2 ) & = ⁻¹ ( 2 + 2 2 - 2 ) & = ⁻¹ ( + - ) & = ⁻¹ ( 1+ 1- ) & = ⁻¹ ( ( 4 + ) ) & = 4 + & = 4 + 1 2 ⁻¹ x^2 aligned

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