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In order for you to claim any education tax benefit you must be able to claim your daughter as a dependent.
If there are qualified education expenses for your dependent during a tax year, either you or your dependent, but not both of you, can claim credit for your dependent's expenses for that year.
See Who Can Claim a Dependent's Expenses
"If you claim an exemption on your tax return for an eligible student who is your dependent, treat any expenses paid (or deemed paid) by your dependent as if you had paid them."
You can and should claim the education expenses that were paid by your daughter that you are allowed claim as a dependent on your tax return.
Please ask if you need clarification.