We present an angle-resolved photoelectron spectroscopy study of the changes in the electronic structure of electron-doped Ba(Fe1−xCox)2As2 across the superconducting phase transition. By changing the polarization of the incoming light, we were able to observe the opening of the gap for the inner hole pocket α and to compare its behavior with the outer holelike band β. Measurements along high-symmetry directions show that the behavior of β is consistent with an isotropic gap opening, while slight anisotropies are detected for the inner band α. The implications of these results for the s± symmetry of the superconducting order parameter are discussed, in relation to the nature of the different iron orbitals contributing to the electronic structure of this multiband system.