Online secondary path modeling is appealing for most active noise control systems due to its benefit of effective tracking of the varying acoustic environment and possible variation of the control sources and sensors. However, the usually utilized additive noise method inevitably leads to the increase of residual noise. Recently we have found that it is possible to model the secondary path without any auxiliary noise as long as the noise to be controlled is not of line spectral property. In this paper, we further extend the analysis and theoretically prove that even for line spectral noise, it is feasible to realize online secondary path modeling using only the output of the control source while exerting active control simultaneously. Simulations using measured impulse responses validate the effectiveness of the proposed simultaneous control and modeling scheme.