They're both optional, so the player can either choose to leave his spells normal, make them 1/2 normal, 1/2 Force (applying only Force-Charged), make them 1/2 Sonic and 1/2 Electric (applying only BoTT), or make them 1/4 Sonic, 1/4 Electric, 1/2 Force (applying BoTT first, then applying Force-Charged). If he applies Force-Charged first, then it effectively becomes over-written by BoTT and deals 1/2 Sonic, 1/2 Electric, and 0 force, according to the RAW of that feat.
Note that splitting up the energy damage into resistable types isn't optimal, since both Sonic and Electric resistance would apply (albeit in smaller quantities), so if he just wants BoTT for the split damage types, definitely suggest he doesn't take that feat.