Connectedness of the Arnold tongues for double standard maps

We show that the Arnold tongues of the family of double standard maps f_{a,b}(x) = 2x + a + (b/pi) sin(2 pi x), are connected. This proof is accomplished in the complex domain by means of quasiconformal techniques and depends partly upon the fact that the complexification of f_{a,b} has only one critical point taking symmetry into account.