Answer
See anwer below.
Work Step by Step
$COP_R=\dfrac1{\frac{\dot{Q}_H}{\dot{Q}_L}-1}$
$\left (\frac{Q_H}{Q_L}\right)_{rev}=\frac{T_H}{T_L}$
$COP_{R,rev}=\dfrac1{\frac{T_H}{T_L}-1}$
If they are reversible and operate between the same reservoir temperatures, they must have the same COP.
