2016 · Q76
If 2y cosθ = x sinθ and 2x sinθ − y cosθ = 3, then what is x² + 4y² equal to?
Elementary MathematicsTrigonometry
- A1
- B2
- C4
- D8
Explanation
The two equations reduce to x·sinθ = 2 and y·cosθ = 1, but θ itself remains free — so x²+4y² = 4csc²θ+4sec²θ is not uniquely determined (its minimum is 16, above every listed option). The stem as printed admits no unique answer. Note: key disputed — verify against the official UPSC key.