You'll notice I've blasphemed by pluralizing in my title, but I'm not talking about that holy trinity. The path to cooking salvation includes many deities, and I'm going to cover just a few here.
In New Orleans, so many recipes begin with the sautéing of chopped onion, celery and bell pepper that the three became known as the holy trinity in the cuisine of that very Catholic city. There are a great many other elements to New Orleans cooking, including local seafood, local coffee, a roux the color of chocolate, ground sassafras root known as filé (feelay), ham stock, turtle eggs, and on and on -- but everybody in New Orleans knows the holy trinity, intimately.
Other cooking styles require other basic ingredients, and interestingly they come in threes as often as not. To cook Italian, you must have this three on hand: Olive oil, Parmagiano Reggiano cheese, and garlic. A tomato also helps (canned is allowed, or in paste form). Other cheeses can be added, juice of a lemon is often added at serving time, and of course either red or white wine often enhances the dish. But everything from salad to meat requires a nodding acquaintance with the holy trinity of Italian food.
Basic food can be made to seem Asian with the addition of this three -- Toasted sesame oil, soy sauce, and grated fresh ginger root. I have added this trinity to slaw, to stove-top-rice-based casseroles, to vegetables and meats with equal success. A real specialist in Chinese, Japanese, or Thai cooking would suggest a range of other additions, but if you have the Asian trinity in the mix, you're getting there. Garlic and honey add something to Chinese; cilantro and lime at the finish make Thai. I know there's more to it than that, but I'm talking basics.
When I want to make a dish with a Mexican flair, I add some cumin, some Monterey Jack cheese, and I might squeeze a fresh lime over all. It's not a holy trinity, and it's more of a finish than a basic, and I don't know if it's really Mexican, but it will pass. It's not take-out, and the amounts are up to you.
God bless good cooking!