Is it permissible for a woman to tear her clothes in front of her husband when she is in a state of extreme anger, and is she sinful for that?

The questioner sinned by what she did, and it is not proper for a Muslim to do anything of the sort, because it is a response to the call of Satan, who takes control of a person in a state of anger. The Prophet, peace and blessings be upon him, advised against anger, so she should not return to this act, and she should repent to God and apologize to her husband.