A trigonometric identity is a mathematical equation that involves trigonometric functions, such as sine, cosine, and tangent, which holds true for all values of the variables involved. These identities are useful in simplifying expressions and solving equations in various fields, including physics and engineering. Common examples of trigonometric identities include the Pythagorean identities, angle sum and difference identities, and double angle identities. Understanding these identities helps in analyzing periodic phenomena, such as waves and oscillations, making them essential tools in both mathematics and applied sciences.