2020 · Q59
If 0 < α, β < 90° such that cos(α − β) = 1, then what is sinα − sinβ + cosα − cosβ equal to?
Elementary MathematicsTrigonometry
- A−1
- B0
- C1
- D2
Explanation
cos(alpha-beta) = 1 with alpha, beta in (0, 90) degrees forces alpha = beta, making sin(alpha)-sin(beta)+cos(alpha)-cos(beta) = 0. Hence option (B). Geometrically, the cosine of a difference equals 1 only when the two angles coincide.