2021 · Q45
Let cos α + cos β = 2 and sin α + sin β = 0, where 0 ≤ α ≤ 90°, 0 ≤ β ≤ 90°. What is the value of cos 2α − cos 2β?
Elementary MathematicsTrigonometry
- A0
- B1
- C2
- DCannot be determined due to insufficient data
Explanation
Since each cosine is at most 1, cos α + cos β = 2 forces cos α = cos β = 1, so α = β = 0° (this also satisfies sin α + sin β = 0). Then cos 2α − cos 2β = 1 − 1 = 0. Hence option A.