Example of what I mean:
Theorem: $\sin^2(\theta) + \cos^2(\theta) = 1$
Proof: [before this, your reader should know what trig functions are, and why they relate to triangles]The relationship between certain transcendental functions ($\sin$ and $\cos$) is quadratic, specifically it resembles a pythagorean identity. [here you could stop reading and move on and use the theorem on faith] More specifically, if we think of these functions as representing the sides of a right triangle with hypotenuse $1$, then this identity is a consequence of the pythagorean theorem. We will show that this is pre…