In a , angle is greater than angle . If the measures of angles and satisfy the equation , then the measure of is
- A.
- B.
- C.
- D.
Show answer and solution
Correct option: C
Solution
The equation 3sin x - 4sin³x = k means sin(3x) = k. So both A and B satisfy sin(3A) = sin(3B) = k.
Since A ≠ B, we need sin(3A) = sin(3B) with 3A ≠ 3B, which gives 3A + 3B = π (the supplementary case), so A + B = π/3.
Therefore C = π - (A + B) = π - π/3 = 2π/3.
Since A ≠ B, we need sin(3A) = sin(3B) with 3A ≠ 3B, which gives 3A + 3B = π (the supplementary case), so A + B = π/3.
Therefore C = π - (A + B) = π - π/3 = 2π/3.
[1990]