Prove that tan4x= (4tanx(1-tan^2x)) / 1-6tan^x+tan^4x

we know tan2Q = 2tanQ / 1-tan^{2}Q

using this formula,

tan4x = tan2.(2x)

=2tan2x / 1-tan^{2}2x

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

simplify to get. , 4tanx(1-tan^{2}x) / 1-6tan^{2}x+tan^{4}x.