2021 · Q56
If x = m secA + n tanA and y = m tanA + n secA, then what is x² − y² equal to ?
Elementary MathematicsTrigonometry
- Am² − n²
- Bm² + n²
- Cm² + n² − mn
- Dm² − n² + mn
Explanation
Expanding, x² − y² = m²sec²A + 2mn·secA·tanA + n²tan²A − m²tan²A − 2mn·tanA·secA − n²sec²A. The cross terms cancel, leaving (m² − n²)(sec²A − tan²A) = m² − n² since sec²A − tan²A = 1. This is option (a).