Can I claim the Hope credit and lifetime learning credit for the same student?
No, the Hope credit and lifetime learning credit cannot both be claimed for the same student at the same time. If you are in a position to claim either credit for a student, you should calculate which one works to better lower your tax burden and claim that one. In addition, remember that the Hope credit can only be claimed for a student’s first two years of post-secondary education, so if you do not claim that credit in the applicable years, you will lose the ability to ever claim that credit (but if the lifetime learning credit puts you in a better position, by all means, take it instead).
Note that you can claim both credits on one return, you just can’t claim both of them for the same student. So if you have two children, one a college freshman and one a college senior, assuming you otherwise meet the credits’ requirements, you could claim a Hope credit for the freshman and a lifetime learning credit for the senior.