2023 · Q6
For what relation between a and b is the equation sin θ = (a + b) / (2√(ab)) possible?
Elementary MathematicsTrigonometry
- Aa = b
- Ba ≤ b
- Ca ≥ b
- Da > b
Explanation
Need |(a+b)/(2 sqrt(ab))|<=1. By AM-GM, (a+b)/2>=sqrt(ab) for a,b>0, so the ratio is >=1. Equality (hence a valid sine) holds only when a=b. Option (a).