Trigonometric identities are mathematical equations that involve the functions of angles, such as sine, cosine, and tangent. These identities express relationships between these functions and are true for all values of the angles involved. They are essential tools in trigonometry, helping to simplify expressions and solve equations. There are several key types of trigonometric identities, including Pythagorean identities, reciprocal identities, and angle sum identities. Each type serves a specific purpose, allowing mathematicians and students to manipulate and understand trigonometric functions more effectively. Mastering these identities is crucial for solving problems in various fields, including physics and engineering.