我这个方法跟传统的证明方法不一样,但还是证明成立,不知你老师是否认可
tan2x-tan x - tanx / cos 2x
=tan2x-tanx(1+1/cos2x)
=tan2x-tanx(cos2x+1)/cos2x
=tan2x-tanx*2cos^2x/cos2x
=tan2x-sinx/cosx*2cos^2x/cos2x
=tan2x-2sinxcosx/cos2x
=tan2x-sin2x/cos2x
=tan2x-tan2x
=0
即
tan2x-tan x - tanx / cos 2x=0
所以
tan2x-tan x = tanx / cos 2x