There's a formula: another = an + other. Think of it as of an article plus the word "other" that have historically merged into one word. Grammar requires some article before "other book"; either "the" or "a." Depending on the context, you get either "You need to buy the other book" (if, for instance, the guy bought only the first book out of the set of two) or "You need to buy an_other book ...
A good example for this is a cube with 6 sides. And that is also the reason why you should use 'on the other hand' but 'on another side'. But I indicate that 'on the other side' and 'on the other hand' are just the same due to the use of 'other' here.
The difference between "the other" and "another" in the phrases "from one cook to the other" and "from one cook to another" is basically the same one that distinguishes "the X" from "a [or an] X": The phrase "from one cook to the other" implies that the speaker or writer has already introduced two specific cooks to the hearer or reader and is now referring to those specific persons. The phrase ...
A year ago, Marcus Claycomb spoke at FireFusion 2024 about the benefits of artificial intelligence (AI) during emergency response. This year, Claycomb was joined by colleague Kjeld Linstead, to futher ...