How to repair my ceiling tape that's coming loose?

The best way it to remove the loose tape and re-tape and mud the area. You can use the traditional paper tape or the self-sticking mesh tape. For most dyi-ers the mesh tape is easiest. There are videos around to show you how,

simply use dap painters chaulk, fill in the crack under the tape with chaulk then use a putty knife to squeeze it flat. use a wet cloth or papers towels to wipe off the excess that squeezed out check on it after a while to make sure it remains flat. then paint when set!

This link gives a step-by-step overview of what to do:

https://www.wikihow.com/Repair-Drywall-Tape-That-Is-Separating-from-Your-Walls

I'd suggest searching Youtube for some videos as well if you're not familiar with using drywall compound in corners.

We are using small molding to cover it up since our ceiling is textured. It will be flat on the ceiling. It looks nice and really doesn't stick out or look out of place. My hubby carefully scraped the texture off where the molding is going. We're in process of putting it up now in our Master Bath. The molding is flat on one edge with a slight decorative edge that's basically a small slanted cut and another flat edge. Figured simple design was better. I will put cove molding in other areas of house ... but will be using in hall, other bath, and bedrooms. We chose the "plastic" molding.

I have put "mud" under the loose tape, then a couple staples to hold it in place and more mud on top.