I've been asked to derive the eigenfunctions for the infinite square well, but by using boundaries of $L/2$ and $-L/2$ instead of $0$ and $L$
I'm happy with the general solution found using the TISE
and that the wavefunction must be zero at the boundaries:
however everywhere I've looked the next step involves using a boundary at $x=0$ to show that
in order to remove the $\cos$ term, which I can't so simply do here since neither of my boundaries are at $x=0$.
It seems without doing that I'm left with two equations and 3 unknowns.