Help Prove this Tan3x = ((3tanx-tan^3x) / (1-3tan^2x))?

Question

Help Me prove this

Answer 1

tan(A +B) = tanA + tanB/(1- tanA*tanB) .........................(1)


(you know this, right?)
Put A = B = x in (1)
We get tan(2x) = 2*tan(x)/(1-tan^2 (x)) ...........................(2)

Now put A = 2x, B=x in (1) ,using relation (2).
We get tan(3x) = [2tan(x)/(1-tan^2(x)) + tan(x)]/[ 1 - {2tan^2(x)}/{1- tan^2(x)}]
Simplifying( I know this looks tough but put pen to paper - and you'll see how simple it is.),
we get

tan(3x) = [3 tan(x) - tan^3(x)]/[1 - 3 * tan^2(x)]

Answer 2

Tan 3x Identity

Answer 3

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