$\sin^2\theta + \cos^2\theta$ equals:

The **Pythagorean identity** $\sin^2\theta + \cos^2\theta = 1$ holds for every real $\theta$. It comes from Pythagoras applied to the unit circle: any point on it has coordinates $(\cos\theta, \sin\theta)$ with distance 1 from origin, so the sum of squared coordinates is 1. Companion identities: - Dividing by $\cos^2\theta$: $1 + \tan^2\theta = \sec^2\theta$. - Dividing by $\sin^2\theta$: $\cot^2\theta + 1 = \csc^2\theta$.