Here is an excerpt from the book "The Cichlid Fish, Natures grand experiment in Evolution" by Dr George Barlow, a leader in cichlid .
research.
"Once in close proximity, each(cichlid) turns off presenting its side to the opponent so the two fish become aligned, side by side, sometimes head next to head, and sometimes head to tail. Now all fins are fully spread. Periodically each fish opens its mouth wide, it passes deep undulations down its body while braking with its pectoral fins to resist the forward force. this behavior is called tail beating, and it may be done in a forceful snap-whip fashion. The result is an imposing display and that washes the opponent with a hefty flow of water that may be perceived as sound."
I have seen this used to judge suitability of a proper mate, or to judge whether to fight or flee with a rival.
Your female may be trying to decide if the male is robust enough to make it worthwhile for her to breed with him.