The Pythagorean identity is one of the most fundamental relationships in trigonometry. It states that for any angle θ, the sum of the squares of sine and cosine equals one: sin²(θ) cos²(θ) = 1. This identity is derived directly from the Pythagorean theorem, which relates the sides of a right triangle. If we consider a point (x, y) on the unit circle (a circle with radius 1 centered at the origin), then x = cos(θ) and y = sin(θ). By the definition of the circle, x² y² = 1², which becomes cos²(θ)