The claim of the first books title 'Carrots Love Tomatoes' is worthy of investigation. Do Carrots really love tomatoes and if so do the Tomatoes love them back ?
Carrots and Tomatoes do love each other but it's only 'puppy love'. Inter-planting carrots and Tomatoes requires good timing. Carrots mature differently than tomatoes so your first harvest of Carrots should be when the Tomatoes are still seedlings.
Mature carrots and mature tomatoes sharing the same bed is not really all its cracked up to be. They compete for the same nutrients at pretty much the same time.
Tomatoes protect the carrots from insect predators, they secrete a natural insect deterrent called solanine which deters many insects that are harmful to carrots. However, the solanine and trace phytotoxins emitted by tomatoes can stunt the growth of carrots if planted too close.