@nprofile1q... as others have said, sec, cosec and cot really show their value when you're doing calculus: when I first learned trig we only used sin, cos and tan. But there are other derived trig functions that are of use in e.g. spherical geometry: see https://en.wikipedia.org/wiki/Haversine_formula

Also, I think derived functions were more useful in the days before calculators. Calculating 1/sin(x) by hand is a real pain compared to looking it up in a book of cosec tables.