There are many factors that can cause drywall joints to crack. Interior Moisture (ie, No HVAC air flow), Exterior Moisture (ie, breach or failure of materials from outside), Foundation settlement or Foundation failure (If this is the issue you can forget about the sheetrock and focus elsewhere). Here's our method on repairing such issues. Cut the old tape and compound out and make sure you leave enough indention so that when you add the new tape, compound and then sand it all turns out flat. There are 3 types of drywall tape at the moment that I'm aware of. The regular paper tape, which is strong and cheap but it absorbs moisture and doesn't bond well. The second which we are using in this instructional is fiberglass mesh tape. It is not affected by moisture and becomes fully embedded into the compound. The third is known as Fibefuse tape. It basically combines the previous two. It is paper thin but is also is moisture resistant and gets fully embedded into compound. Without adding tape to this type of repair you are doing nothing to prevent the crack from reappearing. After applying tape, apply joint compound, wait 24 hours and sand with sheetrock sandpaper as flat as possible. Apply a second and third coat if necessary and keep following the previous steps until all is completely flat. Yes this is a 2-3 day job due to drying time. Don't rush this or your results will not look professional. Once flat to touch apply paint, let dry and shine a light and see if you can spot any imperfections. If none exist it will look like there was never even an issue. Cheers!