∵4sin²x-6sinx-cos²x+3cosx=0，
∴4sin²x-cos²x-6sinx+3cosx=0，
∴（2sinx+cosx）（2sinx-cosx）-3（2sinx-cosx）=0，
∴（2sinx-cosx）（2sinx+cosx-3）=0，
∵2sinx+cosx≤

5

，∴2sinx+cosx-3≠0，
∴2sinx-cosx=0，即cosx=2sinx，
∴

cos2x−sin2x

(1−cos2x)(1−tan2x)

=

cos2x−sin2x

(1−cos2x)(1− sin2x cos2x )

=

cos2x−sin2x

(1−cos2x) cos2x−sin2x cos2x

=

cos2x

1−cos2x

=

cos2x−sin2x

1−cos2x+sin2x

=

(2sinx)2−sin2x

sin2x+sin2x

=

3

2