Jesus never tried to trap people, but His enemies tried to trap Him. Ultimately, they expressed their hatred in a night-time arrest, followed by an unfair trial without true evidence being presented leading to a corrupt sentence, physical violence and death. They hated Jesus so much that they wanted Him physically out of the way.
 
But before that, they were attempting to get Jesus to say something which would incriminate Him. At least, they thought, if they had evidence from two or three eye-witnesses, then the accusations might be successful in the court. What they wanted was the death sentence. But blasphemy was not a crime under Roman law ... however, a charge of treason would immediately engage the Governor's attention and he would have to deal with it, most severely.
 
So they started with flattery and then contrived a theological conversation about whether Jesus believed that taxes ought to be paid to support the Roman Empire. If He said they should be paid, then the Jewish people might riot again, (Governor Pilate was developing a reputation for allowing the people to demonstrate in public) and if Jesus was seen to be the cause, they would arrest Him. On the other hand if Jesus said that the tax should not be paid, the Roman official would view that as a treasonable offence.
 
Questions which include flattery often contain a trap; so be careful. On the other hand, questions give you permission to speak for your Lord. As long they were clear in telling the gospel, the apostles found that God always dealt with the trap and gave them boldness (Acts 4:18-20). The challenge for us is learning how to use questions well in promoting the gospel. That may take some time and experience - and can only be effective if the Holy Spirit is allowed to be active in our hearts. So do not be afraid of hostility even though you may sense a trap. Keep on proclaiming Christ. Let the Lord deal with your enemies and yourself.