Option 1 -> cajole means to persuade someone gently through flattery or persistent urging, which is exactly what coax means.
Option 2 -> pacify means to calm or soothe someone who is angry or upset, not to persuade them.
Option 3 -> force means to compel someone against their will using power or threats, which is much stronger than coax.
Option 4 -> motivate means to inspire or encourage, but lacks the gentle persuasion aspect of coax.
Hence, Option 1: cajole -> Both "coax" and "cajole" involve gently persuading or urging someone to do something through persistent, soft pressure or flattery, making them perfect synonyms -> correct