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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.

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