Answer :

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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