Why do political and religious rulers such as Pepin and the pope often cooperate?

Political and religious rulers like Pepin and the pope often cooperate to consolidate power and legitimacy. By aligning with religious authority, political leaders gain moral support and divine sanction for their rule, while religious leaders can secure protection and resources for their institutions. This symbiotic relationship helps maintain social order and reinforces the authority of both parties, thereby stabilizing their respective realms. Additionally, their cooperation often serves to unify followers under a common cause or belief system, strengthening their influence.