Q. Assume an economy is in a liquidity trap.

A. Write an equation expressing interest rate parity under a fixed exchange rate regime.

Answer: Liquidity trap entail R = 0.  R = 0 = R* + (E^e - E)/E.

B. Assume E^e is fixed.  Suppose that the central bank raises the domestic money supply so as to depreciate the currency temporarily (that is, to raise E currently but return the rate to Ee later).  Show that E cannot be raised.

Answer:  Ever since R = 0 the equation in part A the interest parity condition implies E = E^e / (1- R*) as E^e and R* are fixed E can't change.