Answer No.
The ability of the parent of a high school student to claim the credit or deduction is limited. If these courses are provided by an eligible college, this cost qualifies for the Lifetime Learning Credit (LLC). The school must have policy of granting college credit for that course, already taken, if the student ever enrolls there. In other words, it is a requirement that the course be a college credit course, even if the student isn't currently a college student. It’s not that the student is post secondary, it’s that the course is post secondary. Books are not a qualifying expense, unless included in the course fee.
Alternatively, such courses qualify for the Tuition & Fees deduction, instead of the LLC, but only if tuition is paid to the college and not the high school.
High school students are not usually eligible for the more generous American Opportunity Credit, unless they are officially enrolled as a degree candidate. From pub 970: "Example 3. During the 2015 fall semester, Larry was a high school student who took classes on a half-time basis at College X. Larry wasn't enrolled as part of a degree program at College X because College X only admits students to a degree program if they have a high school diploma or equivalent. Because Larry wasn't enrolled in a degree program at College X during 2015, Larry wasn't an eligible student for tax year 2015." Reference: https://www.irs.gov/publications/p970/ch02.html
