If sin α + sin β = 0 = cos α + cos β , where 0 β α 2 π , then which one of the following is correct?

Question

If sin α + sin β = 0 = cos α + cos β , where 0 β α 2 π , then which one of the following is correct?, α = π − β, α = π + β, α = 2 π − β, 2 α = π + 2 β

MARKS App · Accepted Answer

sin α + sin β = 0 = cos α + cos β sin α + sin β = 0 ⇒ sin α = − sin β ⇒ sin α = sin ( π + β ) ⇒ α = π + β

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