Hi, and welcome to the forum!!

The trichlor tabs are going to do essentially the same thing as your dichlor does--adds chlorine, pushes pH down, and adds CYA. They are not necessary, but if used correctly, they do have their place in pool care. However, as Watermom said, without seeing numbers for CYA, pH, and chlorine, we really can't tell you if they will hurt anything or not--same with your dichlor.