The Pythagorean Identities are fundamental relationships in trigonometry that relate the squares of the sine and cosine functions. The most common identity is expressed as sin²(θ) + cos²(θ) = 1, where θ represents an angle. This identity shows that the sum of the squares of the sine and cosine of an angle is always equal to one. There are also two other important identities derived from the first. These are tan²(θ) + 1 = sec²(θ) and 1 + cot²(θ) = csc²(θ). These identities are useful in simplifying trigonometric expressions and solving equations in various mathematical contexts.