I found out that my 13-year-old daughter is smoking by reading a letter she wrote to her cousin. I know what I did is wrong, but she seems so sad lately and she doesn't want to talk to me about it. She tells me that nothing is wrong. I don't know how to tell her I know about her smoking without losing her trust.
Generally teens have a right to privacy, but wise parents who suspect something is wrong sometimes have to exercise their rights and obligations by invading that privacy. I would encourage you to sit down with your daughter and tell her what you did. Then talk about her sadness and how that worries you. Be specific about how her behavior tells you she's sad. Suggest other adults that she could talk to if she doesn't feel comfortable talking with you. Those adults might be the school counselor, an aunt, one of your family friends, her dad, or a grandparent.
You read the letter to understand why she is sad. So, don't talk about the smoking unless she brings it up. My guess is that she will. When she does, keep it short and encouraging. She probably knows your feelings about smoking anyway. You might gently mention that after the initial rush, smoking adds to depression or sadness because of its physical effect on the body.
Usually the best way to re-establish trust is to be open and honest. Teens often don't want to talk with their parents, but parents have to continue talking to their teens.