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JEE Main2015MathematicsInverse Trigonometric FunctionsActual

If f x = 2 tan - 1 x + sin - 1 2 x 1 + x 2 , x > 1 , then f 5 is equal to

Options

  1. Aπ 2
  2. Btan - 1 65 156
  3. Cπ
  4. D4 tan - 1 5

Correct answer

C. π

Step-by-step solution

Substitute tan - 1 x = θ ,   θ ∈ π 4 , π 2 Hence f x = 2 θ + sin - 1 sin 2 θ = 2 θ + π - 2 θ , as θ > π 4 = π

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