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If x ∈ 0 , 1 , then the value of 2 tan - 1 ⁡ 1 - x 2 2 x + 2 cos - 1 ⁡ 1 - x 2 1 + x 2 is equal to

Options

  1. A- π 2
  2. B0
  3. Cπ 2
  4. Dπ

Correct answer

D. π

Step-by-step solution

∴ Let y = 2 tan - 1 ⁡ 1 - x 2 2 x + 2 cos - 1 ⁡ 1 - x 2 1 + x 2 Putting x = tan ⁡ θ As, x ∈ 0,1 ,   θ ∈ 0 , π 4 and π 2 - 2 θ ∈ 0 , π 2 ∴ y = 2 tan - 1 ⁡ cot ⁡ 2 θ + 2 cos - 1 ⁡ cos ⁡ 2 θ = 2 tan - 1 ⁡ tan ⁡ π 2 - 2 θ + 2 cos - 1 ⁡ cos ⁡ 2 θ = 2 π 2 - 2 θ + 4 θ = π

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