Trigonometric identities are mathematical equations that involve the functions of angles, such as sine, cosine, and tangent. These identities express relationships between these functions, allowing for simplifications and transformations in various mathematical problems. They are essential tools in fields like geometry, physics, and engineering. Common examples of trigonometric identities include the Pythagorean identity, which states that sin²(θ) + cos²(θ) = 1, and the angle sum identities, which help calculate the sine and cosine of the sum of two angles. Mastering these identities is crucial for solving trigonometric equations and analyzing periodic phenomena.