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NTA Abhyas JEE Main2020MathematicsInverse Trigonometric FunctionsPractice

If sin ⁡ cot - 1 ⁡ 1 - x = cos ⁡ tan - 1 ⁡ - x , then x is

Options

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

Correct answer

B. 1 2

Step-by-step solution

sin ⁡ cot - 1 ⁡ 1 - x = cos ⁡ tan - 1 ⁡ - x Let, cot - 1 ⁡ 1 - x = θ ⇒ cot ⁡ θ = 1 - x ⇒ sin ⁡ θ = 1 2 - 2 x + x 2 Let, tan - 1 ⁡ - x = ϕ ⇒ tan ⁡ ϕ = - x ⇒ cos ⁡ ϕ = 1 1 + x 2 ∴ sin ⁡ θ = cos ⁡ ϕ ⇒ 1 2 - 2 x + x 2 = 1 1 + x 2 ⇒ 1 + x 2 = 2 - 2 x + x 2 ⇒ x = 1 2

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