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Manipal MET2020MathematicsInverse Trigonometric Functions

The value of ⁻¹ ( 1+ x + 1- x 1+ x - 1- x ) is equal to

Options

  1. Ax 3
  2. Bx 4
  3. C1
  4. Dx 2

Correct answer

D. x 2

Step-by-step solution

Let l= ⁻¹ ( 1+ x + 1- x 1+ x - 1- x ) aligned & = ⁻¹ [ ( x 2 + x 2 )^2 + ( x 2 - x 2 )^2 ( x 2 + x 2 )^2 - ( x 2 - x 2 )^2 ] & = ⁻¹ ( x 2 + x 2 + x 2 - x 2 . x 2 + x 2 - x 2 + x 2 ) . & = ⁻¹ ( 2 x 2 2 x 2 )= ⁻¹ ( x 2 )= x 2 aligned

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