Prove $\sin^2\theta + \cos^2\theta = 1$ How do you prove the following trigonometric identity: $$ \sin^2\theta+\cos^2\theta=1$$
I'm curious to know of the different ways of proving this depending on different characterizations of sine and cosine.

$$\large \sin^2\theta + \cos^2\theta
=\sin\theta\sin\theta+\cos\theta\cos\theta
=\cos(\theta-\theta)
=\cos0
=1$$
