Patching and Plastering - Help repairing my bathroom ceiling without having to paint

I have a regular textured drywall ceiling in my master bathroom. The house is about 13 years old and some of the tape around the edges of the ceiling above the shower have started to come up due to steam from the shower.

I am in the process of getting my house ready to go on the market and I want to fix this as cheap as possible. is there a way to patch/reglue the corners without having to repaint. If I have to repaint the ceiling; I will also have to repaint the entire master bedroom ceiling which is vaulted. (don't want to do this.

I also thought about putting up crown molding, but I don't know if it will look good.

I'd appreciate some input on whether the corner strips can be replaced without painting or whether they can be reglued?

Thanks

Sorry, the only thing I can think of is to cut out the part that's drooping, mud, prime & paint. I know, not what you wanted to hear.

What kind of texture do you have?

Stucco texture. (not the popcorn type ceiling)

You might be able to use a little caulking to glue and hide the loose tape but the correct way would be to remove the loose and retape, finish and texture. Crown moulding can be difficult to fit on vaulted ceilings.