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CDS 2023 · PYQ · Trigonometry · medium

For what relation between a and b is the equation sin θ = (a + b)/(2√(ab)) possible?

  1. A.a > b
  2. B.a ≥ b
  3. C.a = b✓ Correct
  4. D.a ≤ b

Explanation

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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