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JEE Main2017MathematicsInverse Trigonometric FunctionsActual

A value of x satisfying the equation sin ⁡ cot - 1 ⁡ 1 + x = cos ⁡ tan - 1 ⁡ x , is:

Options

  1. A- 1 2
  2. B0
  3. C- 1
  4. D1 2

Correct answer

A. - 1 2

Step-by-step solution

sin cot - 1 ( 1 + x ) = cos tan - 1 x Let, cot λ = 1 + x tan β = x ⇒ sin λ = cos β ⇒ 1 x 2 + 2 x + 2 = 1 1 1 + x 2 ⇒ x 2 + 2 x + 2 = x 2 + 1 ⇒ x = - 1 / 2

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