Given, 2 tan α = 3 tan β

From here we get, ------ (1)

Now consider tan (α - β),

The expansion of tan (α - β) is given by

As we already know the value of tan α from equation (1), we have,

[ by using ]

Multiplying and dividing the equation with 2

[using sin2θ = 2 sinθ cosθ]

In the denominator adding and subtracting 1

[using cos2θ = 2cos²θ – 1]

Hence, in the question the answer matches with option A.