Prove that ` tan (2 tan^(-1) x ) = 2 tan (tan^(-1) x + tan^(-1) x^(3))

1.	Prove that ` tan (2 tan^(-1) x ) = 2 tan (tan^(-1) x + tan^(-1) x^(3))`.
Answer» L.H.S `= tan(2 tan^(-1)x) = tan{ tan^(-1) .(2x)/(1-x^(2))}=(2x)/(1-x^(2))` `R.H.S = 2 tan {tan ^(-1) x+ tan ^(-1)x^(3)}` ltbr. `= 2 tan { tan^(-1) .(x+x^(3))/(1-x.x^(3))} = (2x(1+x^(2)))/((1-x^(2))(1+x^(2)))=(2x)/(1-x^(2))` L.H.S= R.H.S

Discussion

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