hi!gracey (sweet name)
your starting is absolutly fine.
(2tan x / 1-tan^2 x) - tan x
now what you should really do is take tanx common
tanx[(2/(1-tan^2x)-1]
now use
tan^2x=(1-cos2x)/1+cos2x
after substituting we get
tanx[2/(1-{(1-cos2x)/1+cos2x})-1]
=tanx[{(1+cos2x)/cos2x}-1]
=tanx[1/cos2x]
=tanxsec2x
hence proved