Question

If sinα + sinβ = 0 = cosα + cosβ , where 0 < β < α < 2π , then which one of the following is correct?

a. α = π - β

b. α = π + β

c. α = 2π - β

d. 2α = π + 2β

Answer 1

Correct option b. α = π + β

Explanation:

(sinα + sinβ)2 + (cosα + cosβ)2 = 0

⇒ 2 + 2cos(α - β) = 0

⇒ cos(α - β) = - 1 = cosπ

⇒ α = π + β