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NTA Abhyas JEE Main2020MathematicsInverse Trigonometric FunctionsPractice

The relation tan - 1 ⁡ 1 + x 1 - x = π 4 + tan - 1 ⁡ x holds true for all

Options

  1. Ax ∈ R
  2. Bx ∈ ( - ∞ , 1 )
  3. Cx ∈ ( - 1 , ∞ )
  4. Dx ∈ ( - ∞ , 2 )

Correct answer

B. x ∈ ( - ∞ , 1 )

Step-by-step solution

Given, tan - 1 ⁡ 1 + x 1 - x = π 4 + tan - 1 ⁡ x RHS = π 4 + tan - 1 ⁡ x = tan - 1 ⁡ 1 + tan - 1 ⁡ x = tan - 1 ⁡ 1 + x 1 - x , if x < 1 ∴ x ∈ ( - ∞ , 1 )

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