解方程:(sin2x+cos2x)/(1-sin^2x-2cos2x)=2

sin2x+cos2x
=1-2sin^2x+2sinxcosx
2-2sin^2x-4cos2x
=-2sin^2x+2-4+8sin^2x
=-2+6sin^2x
即,8sin^2x-2sinxcosx-3=0
5sin^2x-2sinxcosx-3cos^2x=0
(5sinx+3cosx)(sinx-cosx)=0
因为,X属于(π/2,π）
所以5sinx=-3cosx
tanx=-3/5
x=π-arctan(3/5)