Question

Why does `cos(x) = sin(90-x)` for `x` such that `0°<x<90°`?

Answer 1

Use trig identity:
`sin (a - b) = sin acos b - sin bcos a`
In this case:
`sin (90 - x) = sin 90cos x - sin xcos 90`
Unit circle -->
`sin 90 = 1, and cos 90 = 0.`
Therefore:
`sin (90 - x) = cos x`. Proved.