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JEE Advanced2008MathematicsInverse Trigonometric FunctionsActual

If 0 < x < 1 , then 1+x^2 [ x ( ⁻¹ x )+ ( ⁻¹ x ) ^2-1 ]^ 1 2 is equal to

Options

  1. Ax 1+x^2
  2. Bx
  3. Cx 1+x^2
  4. D1+x^2

Correct answer

C. x 1+x^2

Step-by-step solution

We have, 0 Now, aligned & 1+x^2 [ x ( ⁻¹ x )+ ( ⁻¹ x ) ^2-1 ]^ 1 / 2 &= 1+x^2 [ x x 1+x^2 + 1 1+x^2 ^2-1 ]^ 1 / 2 &= 1+x^2 [ ( 1+x^2 1+x^2 )^2-1 ]^ 1 / 2 &= 1+x^2 [1+x^2-1 ]^ 1 / 2 &=x 1+x^2 aligned

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