Either you or your dependent (but not both) can claim the American opportunity credit or the lifetime learning credit.
If you claim an exemption on your return for your dependent, only you can claim the credit. Treat any expenses paid by your dependent as paid by you.
If you do not claim an exemption on your return for your dependent, your dependent can claim the education credit. Your dependent can use expenses you or anyone else pays for education expenses on his or her behalf.