因为f（ x ）=cos2x /cosx-sinx
=[（cosx)^2-(sinx)^2]/(cosx-sinx)
=[(cosx+sinx)(cosx-sinx)]/(cosx-sinx)
=cosx+sinx
=根号2（根号2/2sinx+根号2/2cosx)
=根号2(sinxcosπ/4+cosxsinπ/4)
=根号2sin(x+π/4)
所以f（ x ）=cos2x /cosx-sinx的值域为【-根号2,根号2】.