If α and β are the solutions of s i n x = - 1 2 in 0,2 π and α and γ are the solutions of cos ⁡ x = - 3 2 in 0,2 π , then the value of α + β β - γ is equal to

Step-by-step solution

sin ⁡ x = - 1 2 ⇒ x = 7 π 6 , 11 π 6 cos ⁡ x = - 3 2 ⇒ x = 5 π 6 , 7 π 6 ⇒ α = 7 π 6 , β = 11 π 6 , γ = 5 π 6 ⇒ α + β = 7 π 6 + 11 π 6 = 3 π , β - γ = 11 π 6 - 5 π 6 = π ⇒ α + β β - γ = 3 π π = 3