If tan(α+β) = a, tan(α-β) = b, then the value of tan2α is :

2α = ( α + β ) + ( α - β )

tan2α  =  tan [ ( α + β ) + ( α - β ) ]

= \(\frac{tan( α + β ) + tan ( α - β ) }{ 1 - tan( α + β ) . tan ( α - β )}\)

Put putting values of tan( α + β ) = a & tan( α - β ) = b

= \(\frac{a+ b }{ 1 - a . b}\)