weaver image reject architecture

I found this derivation of IF output for a weaver image reject architecture. However, the step where the image is algebraically eliminated is not clear for me because the terms have different coefficients (Arf/4 and Aim/4).
Is this correct ? Anybody has the algebraic derivation of this topology ?
I'll apreciate.

The suffices RF & IM represent the wanted signal and the image signal on either side of the first local oscillator w1. They are both present at the ouput of the low pass filter as given in expression XA(t).
The amplitudes Arf and Aim are halved because half of the input power is in the sum terms which are rejected by the low pass filter.

The second mix with w2, which should be at the cut off frequency of the low pass filter is given by Xc(t). Again the signal level is halved, we are only interested in the differences.

The signal at D XD(t) is derived in the same way as XC but this time multiplying by cos instead if sin.
This gives ignoring the amplitude terms which are all equal any way.
. - cos( RF signal ) + cos( Image signal ) at C
and cos( RF signal ) + cos( Image signal ) at D

Subtracting C from D as shown in the diagram gives an output of 2*cos(RF signal)

If the subtracter were substituted for a summing network the output would be
2*cos( Image signal ).

A practical implimentation is quite difficult unless using DSP, as the tracking of the two low pass filters sets the ultimate image rejection. Assuming accurate quadrature between the oscillators.

Hope this makes it a little clearer

peter