f(x)=cos2x/(1-tanx)
=(cosx-sinx)(cosx+sinx)/[(cosx-sinx)/cos]
=(cosx+sinx)cosx
=1/2[2cosx^2-1+2sinxcosx+1]
=1/2(cos2x+sin2x)+1/2
=√2/2cos(2x-π/4)+1/2
cos(2x-π/4)∈[-1.1]
所以f（x）属于[(1-√2)/2,(1+√2)/2]