The value of 2 α + β   0 < α ,   β < π 2 , satisfying the equation cos ⁡ α cos ⁡ β cos ⁡ α + β = - 1 8 is equal to

Step-by-step solution

From the given relation, 2 cos ⁡ α cos ⁡ β cos ⁡ α + β = - 1 4 c o s α + β + c o s α - β c o s α + β = - 1 4 Let, c o s α + β = t t + c o s α - β t = - 1 4 ⇒ 4 t 2 + 4 t c o s α - β + 1 = 0 The roots will be real if D ≥ 0 ⇒ 16 c o s 2 α - β - 16 ≥ 0 ⇒ 16 c o s 2 α - β ≥ 16 ⇒ c o s 2 α - β ≥ 1 ⇒ c o s 2 α - β = 1 ⇒ α