JEE Main20241 Feb 2024Morning ShiftMathematicsTrigonometric Ratios & IdentitiesActual
If tan A = 1 x x 2 + x + 1 , tan B = x x 2 + x + 1 and tan C = x − 3 + x − 2 + x − 1 1 2 , 0 < A , B , C < π 2 , then A + B is equal to:
Options
- AC
- Bπ − C
- C2 π − C
- Dπ 2 − C
Correct answer
A. C
Step-by-step solution
Given, tan A = 1 x x 2 + x + 1 , tan B = x x 2 + x + 1 and tan C = x − 3 + x − 2 + x − 1 1 2 = 1 + x + x 2 x x We know that, tan A + B = tan A + tan B 1 − tan A tan B ⇒ tan A + B = 1 x x 2 + x + 1 + x x 2 + x + 1 1 − 1 x 2 + x + 1 ⇒ tan A + B = 1 + x x 2 + x + 1 x 2 + x x ⇒ tan A + B = 1 + x x 2 + x + 1 x 2 + x x ⇒ tan A + B = x 2 + x + 1 x x ⇒ tan A + B = tan C ⇒ A + B = C