2021 · Q60
If the equation x² + y² − 2xy sin²θ = 0 contains real solution for x and y, then
Elementary MathematicsTrigonometry
- Ax = y
- Bx = −y
- Cx = 2y
- D2x = y
Explanation
Treat it as a quadratic in x: the discriminant is 4y²sin⁴θ − 4y² = 4y²(sin⁴θ − 1). Real x requires this to be ≥ 0, and since sin⁴θ ≤ 1 this forces sin²θ = 1. Then the discriminant is 0 and x = y·sin²θ = y. Hence option A.