Prove that tan4x=4tanx(1-tan²x)/1-6tan²x+tan⁴x.

Answer 1

I think the best way to start would be

tan 4x = 2*tan 2x/(1-tan^2 2x)

= 2(2tanx/(1-tan^2x)) / (1-(2tanx/(1-tan^2x))^2)

Now place top and bottom over a common denominator of (1-tan^2x)^2
and you should see things going where you want them.