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MHT CET202415 May 2024Evening ShiftMathematicsInverse 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^2 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

Let ⁻¹ x= , then x= and aligned & 4 2 [ 0 x 1 0 1] & 1+x^2 [ x ( ⁻¹ x )+ ( ⁻¹ x ) ^2-1 ]^ 1 2 = & 1+x^2 [ + ^2-1 ]^ 1 2 = & 1+x^2 ( ^2 + ^2 )^2-1 ]^ 1 2 = & 1+x^2 cosec ^2 -1 = & 1+x^2 | | = & ( 1+x^2 )|x| = & x 1+x^2 aligned [ 0 x 1]

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