If 2 tan α = 3 tan β, prove that tan (α - β)

Given: 2 tan α = 3 tan β



Proof:


Take LHS:


tan α – tan β














{ sin 2x = 2(sin x)(cos x)}



{ 2 cos2 x = 1 + cos 2x & 2 sin2 x = 1 – cos 2x}




= RHS


Hence Proved


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