Comment by syphia

A case study of myself as an overeager math student:

I used to focus so much on finding "elegant" proofs of things, especially geometric proofs. I'd construct elaborate diagrams to find an intuitive explanation, sometimes disregarding gaps in logic.

Then I gave up, and now I appreciate the brutal pragmatism of using Euler's formula for anything trigonometry-related. It's not a very elegant method, if accounting for the large quantity of rote intermediate work produced, but it's far more effective and straightforward for dealing with messy trig problems.