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JEE Main2015MathematicsInverse Trigonometric FunctionsActual

Let tan - 1 y = tan - 1 x + tan - 1 2 x 1 - x 2 , where x < 1 3 ,Then a value of y is

Options

  1. A3 x + x 3 1 + 3 x 2
  2. B3 x - x 3 1 - 3 x 2
  3. C3 x + x 3 1 - 3 x 2
  4. D3 x - x 3 1 + 3 x 2

Correct answer

B. 3 x - x 3 1 - 3 x 2

Step-by-step solution

Given tan - 1   y = tan - 1   x + tan - 1 2 x 1 - x 2 ,  x < 1 3 = tan - 1   x + 2 tan - 1   x = 3 tan - 1   x ⇒ tan - 1   y = tan - 1 3 x - x 3 1 - 3 x 2 ∴   y = 3 x - x 3 1 - 3 x 2

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