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
- Aπ 6
- Bπ 4
- Cπ 3
- 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 +