See figure attached for the problem statement as well as my attempt.

I'm confused as to how to do part B.

Do they want me to choose two values such as n=1, and n=2, compute their respective eigenfunctions and see if they are orthogonal?

Or do I have to do it for case such as, n=a and n=b?

Also, how do I compute the integral to verify that it's 0? Isn't it just going to be sin(something)*sin(somethingdifferent)?

Any ideas?