Was hamlet’s insanity entirely fake? or did he actually become mad at times? cite evidence from acts i, ii, and iii to support your answer

I do not believe that Hamlet's insanity is entirely fake. It seems that it is fake in the beginning of the play when we learn that he is just pretending to be crazy to confuse Claudius. He planned to seek revenge on him. But as Hamlet's character is revealed, it can be said that he actually did become mad at times. When having a conversation with Polonius, Hamlet acted completely mad by saying, “For in the sun breed maggots in a dead dog, being a good kissing carrion-Have you a daughter?”(Hamlet 2.2.95) Hamlet would talk like to to anyone who was close to Claudius. As the play progressed, his madness became more and more evident. In an effort to follow through with his plan, he became very irrational in words and actions.