> [!NOTE] Corollary (Circular property/ Pythagorean property) > For all $x\in\mathbb{R}$, $\cos^{2}x + \sin^{2}{x} = 1$ **Proof**: Set $y=-x$ is addition formula for $\cos$. We know that $\cos(-x) = \cos x$ and $\sin (-x)= -\sin (x)$ so $1 = \cos 0 = \cos (x-x) = \cos(x)\cos(-x)-\sin x\sin(-x)=\cos^{2}x + \sin^{2}x.$