Question

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

Answer 1

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)#