已知2sin²x-cos²x+sinxcosx-4sinx+2cosx=0求(sin2x+1)/(1+cos2x+sin2x)

已知2sin²x-cos²x+sinxcosx-4sinx+2cosx=0求(sin2x+1)/(1+cos2x+sin2x)
已知2sin²x-cos²x+sinxcosx-4sinx+2cosx=0求(sin2x+1)/(1+cos2x+sin2x)

已知2sin²x-cos²x+sinxcosx-4sinx+2cosx=0求(sin2x+1)/(1+cos2x+sin2x)
（2sinx-cosx）（sinx+cosx）-2（2sinx-cosx）=0
（2sinx-cosx）（sinx+cosx-2）=0
因为（sinx+cosx-2）<0
所以（2sinx-cosx）=0
2sinx=cosx
tanx=1/2
(sin2x+1)/(1+cos2x+sin2x)
=(2sinxcosx+sin^2x+cos^2x)/(2cos^2x+2sinxcosx),(分子分母同除以cos^2x)
=(2tanx+tan^2x+1)/(2+2tanx)
=(1+1/4+1)/(2+1)
=3/4