Thanks guys (and gals)
After 5+ years together, both started as less than 1.5 inches, my Purple tang start to beat up my Yellow tang. Tail fin tattered on both fish and the L spike of the yellow tang injured. The Yellow tang was force to go into the rock work. Every time he show his face the Purple would dash over and chase him back into the rock. Both fish were very healthy and fat before all of this started last week.
After observing for 1 week and see that this is not going to stop, I set out my fish trap and got the Purple tang and put him into my Frag tank, (40 gal breeder). This is where he will be until I decide what to do next. I think I can easily trap my Yellow tang.
I really love both of these tangs, and it is hard for me to decide which of these tang to re-home. Why can't they just get along.