please help me solve this. I'm very confused on this topic and my teacher wasn't any help.

sin2x=tanx(2-2sin^2x)

2sinxcosx=(sinx/cosx)(2-2sin^2x) (because sin2x=2sinxcosx and tanx=sinx/cosx)

divide both sides by 2

sinxcosx=(sinx/cosx)(1-sin^2x)

sinxcosx=(sinx/cosx)(cos^2x) (because sin^2x+cos^2x=1

sinxcosx=sinxcosx (because cos^2x/cosx=cosx; you are simplifying)