题目内容：

已知（2sin^2x+sin2x）/(1+tanx)=1/2(π/4

优质解答

（2sin^2x+sin2x）/(1+tanx)
=cosx*（2sin^2x+2cosx*sinx）/(1+tanx)*cosx
=2sinx*cosx(sinx+cosx)/(cosx+sinx)
=2sinx*cosx=sin2x=1/2
(sinx-cosx)^2=sin^2x+cos^2x+2sinxcosx
=1+sin2x=3/2
π/40
sinx-cosx=√(3/2)