Gertrude: unfortunately even basic trig frightens-off quite a few studes so, at the PPL level, I think it's best just to get people using the practical guidance. Those who want to derive the MD and SCA stuff for themselves will do so.
Old,not ...: in my groundschool sessions I have to teach the 1:60 stuff so people can pass the exam, but I hope nobody starts doing the calcs in the air to work out a closing angle. It's far better to avoid awkward sums and use the MDR stuff I described earlier for diversions, or even (heresy!) for all nav calcs, and to use SCA to get back close to the pre-planned track ASAP.
The link I gave earlier shows a simple visual way of using the DI (or any compass rose) to estimate proportions of MD and GS on any heading.
As an aside, the closing angle technique used to be widely taught, but this gets you to fly down a direct line to destination from your off-track position. This new line is one that you haven't planned or checked and may contain dragons, or worse. Clearly, the double track error technique only works to the half way point in its simplest form, using it beyond the half way point requires you to have a sensible serious of "opportunity" fixes noted on your chart so you can use double track error on part of the segment.
SCA is simple and works almost anywhere. The only time it's worth fiddling with it is at speeds of less than about 100kt, when it's better to use half the SCA for twice the time.
HFD