> Why do math students need to know the sine doubling rule? Not so they can calculate with it (they could look that up) but so they can reduce certain expressio

> Why do math students need to know the sine doubling rule? Not so they can calculate with it (they could look that up) but so they can reduce certain expressions to sin(2x). That's why calculus teaches this stuff. Why make math students memorize random trigonometric identities that they'll use once and then immediately forget when you could teach them a more general fact that they can derive the identities from? sin(2x) = Im(cos 2x + i sin 2x) = Im(e^2ix) = Im(e^ix * e^ix) = Im((cos x + i sin x)^2) = Im(cos^2 x + 2i cos x sin x + sin^2 x) = Im(cos^2 x - sin^2 x + 2i cos x sin x) = 2 cos x sin x