A few comments, not so much for your low value book but in general for taping. (Caveat: I'm an interested amateur in paper conservation, not a pro.)
As a general principle, anything you do a document should be as reversible as possible. Not all archival tapes are created equal and there's a reason that the price varies so widely. The cheap ones in Officeworks are likely to give poorer outcomes.
If you are going to tape a completely split cover, tape it lengthwise alone the spine, the way Point Five suggests. The reason it split is that it's brittle, and trying to do 'less harm' by using smaller pieces at odd points could lead to more tearing during handling where the strong tape meets the weak paper.
Any form of adhesive tape, archival or otherwise, bonds the adhesive to the paper, which complicates removal later and would probably require solvents other than water. (See the detailed explanation here.) Even good archival tapes can be a pain to remove. Archive quality Japan paper and paste is always water soluble and is a preferable approach to sealing tears and reinforcing spines.