lim x->0 [(tanx-sinx)/(x-x*cos2x)]
=lim x->0 [sinx(1-cosx)/cosx]/(x(1-cos2x)
=lim x->0 [sinx*2(sin(x/2))^2]/[cosx*x*2(sinx)^2]
=lim x->0 [x*2(x/2)^2]/(x*2x^2)
=1/4