This page (screenshot below) is intended to demonstrate the sum and difference trig identities. I spent some time considering the diagram, trying to produce the identities myself. Finally, I decided to check the author's derivation.
The first thing I noticed is that the derivation at the beginning seems to be unnecessarily complicated. Why not make this a unit circle, with $OD$ and $OE$ equal to $1$?. That bit isn't entirely shown here, because what is keeping me awake is the angle $ODE$ which "we can see from the drawing" is a right angle. Apart from this being a less than rigorous claim about the rather forced red square, angle $ODE$ is at the base of an isosceles triangle, is it not? I see no way it could be construed to be a right angle.
Am I missing something in this nocturnal rambling? Are the sum and difference identities hidden in this diagram in a way that a good night's sleep might reveal in the morning?
