If cot ⁡ α + β = 0 , then sin ⁡ α + 2 β is equal to

Step-by-step solution

Given, cot ⁡ α + β = 0 ⇒ cos ⁡ α + β = 0 ⇒ α + β = 2 n + 1 π 2 , n ∈ I ∴ sin ⁡ α + 2 β = sin ⁡ 2 α + 2 β - α = sin ⁡ [ 2 n + 1 π - α ] = sin ⁡ ( 2 n π + π - α ) = sin ⁡ π - α = sin ⁡ α