What type of fusion occurs in the red giant phase of the star life cycle? How do we know?
Nuclear fusion, its the only kind existent in stars. Spectrographs tell us that.
The enormous mass of stars causes a nuclear fusion first of the hydrogen atoms and then of the helium atoms.
We know because every atom vibrates at a different rate which send out light at that vibration rate (frequency).
The chart above shows the part of the light spectrum associated with each element.