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If sin θ = 1/2 √(x/y) + √(y/x), then it must follow that:

1. x is greater than y
2. x is less than y
3. x is equal to y
4. both x and y are purely imaginary

Correct answer: x is equal to y

Solution

By AM-GM, sqrt(x/y)+sqrt(y/x) >= 2, so (1/2)(sqrt(x/y)+sqrt(y/x)) >= 1. Since sin theta <= 1, equality must hold, which requires sqrt(x/y)=sqrt(y/x), i.e. x = y.

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