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The value of x for which sin ⁡ cot - 1 ⁡ 1 + x = cos ⁡ ( tan - 1 ⁡ x ) is

Options

  1. A1 2
  2. B1
  3. C0
  4. D- 1 2

Correct answer

D. - 1 2

Step-by-step solution

Let, cot - 1 ⁡ x + 1 = θ and tan - 1 ⁡ x = ϕ Now, given equation becomes sin θ = cos ϕ ⇒ 1 1 + x + 1 2 = 1 1 + x 2 ⇒ x + 1 2 + 1 = x 2 + 1 ⇒ x = - 1 2

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