If x sin³θ + y cos³θ = sin θ cos θ and x sin θ − y cos θ = 0, for every θ ∈ (0, π/2), then what is x² + y² equal to?
A.2
B.0
C.1✓ Correct
D.3
Explanation
From second: x sinθ = y cosθ, so x = y cosθ/sinθ. Substitute: y cosθ/sinθ · sin³θ + y cos³θ = sinθ cosθ ⟹ y cosθ(sin²θ+cos²θ) = sinθ cosθ ⟹ y = sinθ. Then x = cosθ. So x²+y² = 1.
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