How do you prove $(1+tanx) tan2x = (2tanx)/(1-tanx)$ ?

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Answer 1 · 2016-03-07T23:55:37

From the identity

$tan(A+B)=[tanA+tanB]/[1-tanA*tanB]$

for $A=B=x$

we have that

$tan(x+x)=2*tanx/(1-tan^2x)=> tan2x=[2*tanx]/[(1-tanx)*(1+tanx)]=> (1+tanx)*tan2x=[2*tanx]/(1-tanx)$

How do you prove (1+tanx) tan2x = (2tanx)/(1-tanx)(1+tanx) tan2x = (2tanx)/(1-tanx)?