CDS 2023 · PYQ · Trigonometry · medium
For what relation between a and b is the equation sin θ = (a + b)/(2√(ab)) possible?
Answer
The correct answer is C: a = b. By AM-GM, (a+b)/(2√(ab)) ≥ 1 with equality iff a = b. Since sin θ ≤ 1, we need equality, i.e., a = b.
- A.a > b
- B.a ≥ b
- C.a = b✓ Correct
- D.a ≤ b
By AM-GM, (a+b)/(2√(ab)) ≥ 1 with equality iff a = b. Since sin θ ≤ 1, we need equality, i.e., a = b.
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