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Referred to the input of the last opamp (without any feedback) the circuit works as an allpass.
This means that for different frequencies the amplitudes remain constant and the phase is shifted as a function of frequency.
This description does not yet include the function of the input bandpass which can be described separately.
Vout1=Vin*[1/(1+jwRC)] >> first-order lowpass
Vout2=-Vin*[jwRC/(1+jwRC)] >> first order highpass.
To proove that the magnitude of the sum is constant and the phase moves from zero to -180deg. you must evaluate the sum of both output signals separately as magnitude and phase.
The calculation is rather straight forward - however a bit involved.
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