For α , β ∈ 0 , π 2 let 3 sin ( α + β ) = 2 sin ( α - β ) and a real number k be such that tan α = tan β . Then the value of k is equal to

Step-by-step solution

Given: 3 sin α + β = 2 sin α - β ⇒ sin α + β sin α - β = 2 3 ⇒ sin α + β + sin α - β sin α + β - sin α - β = 2 + 3 2 - 3 ⇒ 2 sin α cos β 2 cos α sin β = - 5 ⇒ tan α tan β = - 5 ⇒ tan α = - 5 tan β ⇒ k = - 5