Verified answer

Algebraically multiply out the left side:

(cosθ-sinθ)² = cos²θ - 2cosθsinθ + sin²θ

Rearrange:

(cosθ-sinθ)² = cos²θ + sin²θ - 2cosθsinθ

The Pythagorean Identity is cos²θ + sin²θ = 1, so:

(cosθ-sinθ)² = 1 - 2cosθsinθ

The sine double angle identity is 2cosθsinθ = sin2θ, so:

(cosθ-sinθ)² = 1 - sin2θ.

I don't know the answer, but this just confused the hell out of me. This is without a doubt, the most confusing thing i've seen today.