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?

Cannot be determined due to insufficient data

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? Correct Answer 0

Calculation:

⇒ cos α + cos β = 2

Squaring,

⇒ cos²α + 2cosα .cosβ + cos²β = 4......(1)

⇒ sin α + sin β = 0

Squaring,

⇒ sin²α + 2sinα.sinβ + sin²β = 0......(2)

Adding,

⇒ 2cos(α - β) = 2

⇒ cos(α - β) = 1

⇒ α - β = cos^-1(1) = 0

⇒ α = β

⇒ ? = cos 2α - cos 2β

∴ ? = 0

Feb 20, 2025

Related Questions