Efficiently modeling historical information is a critical component in addressing user queries within a conversational question-answering (QA) context, as historical context plays a vital role in clarifying the user's questions. However, irrelevant history induces noise in the reasoning process, especially for those questions with a considerable historical context. In our novel model-agnostic approach, referred to as CoTaH (Consistency-Trained augmented History), we augment the historical information with synthetic questions and subsequently employ consistency training to train a model that utilizes both real and augmented historical data to implicitly make the reasoning robust to irrelevant history. To the best of our knowledge, this is the first instance of research using question generation as a form of data augmentation to model conversational QA settings. By citing a common modeling error prevalent in previous research, we introduce a new baseline model and compare our model's performance against it, demonstrating an improvement in results, particularly when dealing with questions that include a substantial amount of historical context. The source code can be found on our GitHub page.