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99 Percentile Qs Bank for JEE MainMathematicsInverse Trigonometric Functions

2 tan - 1 1 5 + sec - 1 5 2 7 + 2 tan - 1 1 8 =

Options

  1. Aπ 6
  2. Bπ 4
  3. Cπ 3
  4. Dπ 8

Correct answer

B. π 4

Step-by-step solution

Given that, 2 tan - 1 1 5 + sec - 1 5 2 7 + 2 tan - 1 1 8 = 2 tan - 1 1 5 + 2 tan - 1 1 8 + sec - 1 5 2 7 = 2 tan - 1 1 5 + tan - 1 1 8 + sec - 1 5 2 7 = 2 tan - 1 1 5 + 1 8 1 - 1 5 · 1 8 + sec - 1 5 2 7 ∴   tan - 1 A + tan - 1 B = tan - 1 A + B 1 - A B = 2 tan - 1 8 + 5 40 - 1 + sec - 1 5 2 7 = 2 tan - 1 13 39 + sec - 1 5 2 7 = 2 tan - 1 1 3 + sec - 1 5 2 7 = tan - 1 2 × 1 3 1 - 1 3 2 + sec - 1 5 2 7 ∴   2 tan - 1 A = tan - 1 2 A 1 - A 2 = tan - 1 6 8 + sec - 1 5 2 7 = tan - 1 3 4 +

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