The phrase "study at coax" can be replaced with several different synonyms to convey a similar meaning. Some options include "research with encouragement," "learn with gentle persuasion," and "examine with coaxing." These variations all imply a sense of motivation and guidance, suggesting that the act of studying is being facilitated or supported in some way. Other phrases that could be used as synonyms for "study at coax" might include "delve with a nudge," "scrutinize with coaxing," "analyze with gentle urging," or "investigate with gentle prodding." Essentially, any combination of words that suggests a gentle, subtle approach to prompting someone to study or learn could be considered a synonym for "study at coax".