If α and β are the solutions of cot ⁡ x = - 3 in 0,2 π and α and γ are the solutions of cosec ⁡ x = - 2 in 0,2 π , then the value of α - β β + γ is equal to

Step-by-step solution

cot ⁡ x = - 3 ⇒ x = 5 π 6 , 11 π 6 and cosec ⁡ x = - 2 ⇒ x = 7 π 6 , 11 π 6 So, α = 11 π 6 ,   β = 5 π 6 ,   γ = 7 π 6 ⇒ α - β = π and β + γ = 2 π ⇒ α - β β + γ = π 2 π = 1 2