Answer :

Given that,


cos(α + β) = 4/5 …(1)


we know that: sin x = √(1 – cos2x)


sin (α + β) = √(1 – cos2(α + β))


sin (α + β) = …(2)


Also,


sin(α - β) = 5/13 {given} …(3)


we know that: cos x = √(1 – sin2x)


cos (α - β) = √(1 – sin2(α - β))


cos (α - β) = …(4)


tan 2α = tan (α + β + α – β)


We know that:


tan 2α =


tan 2α =


Using equation 1,2,3 and 4 we have –







Hence, tan 2α = 56/33


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