Student problem: Amplification of cascade
Sorry for not having any fine symbols.

But the solution is trivial. You have written that the 2nd transistor pushes current against its base current (no other way available for AC current). Vbe/(rb)=-G*Vbe 

There's 2 possible solutions G=-1/(rb) or Vbe=0. Only the latter is acceptable. Thus the output voltage follows the voltage at the base of the 2nd transistor