If 0 < α , β < π and cos ⁡ α + cos ⁡ β - c o s α + β = 3 2 , then the value of 3 sin ⁡ α + cos ⁡ α is equal to

Step-by-step solution

2 c o s α + β 2 c o s α - β 2 - 2 c o s 2 α + β 2 - 1 = 3 2 ⇒ 4 c o s 2 α + β 2 - 4 c o s α + β 2 c o s α - β 2 + 1 = 0 ⇒ 2 c o s α + β 2 - c o s α - β 2 2 + s i n 2 α - β 2 = 0 ⇒ 2 c o s α + β 2 = c o s α - β 2 and s i n α - β 2 = 0 ⇒ α = β and 2 cos ⁡ α = 1 ⇒ α = π 3   0 < α , β < π So, sin ⁡ α =