There are many synonyms for the phrase "induce to talk/speak," each with its own connotations and shades of meaning. Some options include encourage, coax, persuade, prompt, and cajole. Encourage implies a gentle push or motivation towards speaking, while coax suggests a more persuasive or persistent approach. Persuade and prompt both imply a deliberate effort to convince or propel someone to speak, while cajole suggests a more playful or flattery-based approach. Ultimately, the choice of synonym will depend on the context of the situation and the tone desired, but all these options can be useful for getting someone to open up and communicate.