Which of the following statements is true regarding trigonometric identities?

Trigonometric identities are fundamental equalities that hold true for all values of the angles involved in the functions, not just specific cases. By definition, they are expressions that relate various trigonometric functions to each other, such as the Pythagorean Identity (sin²(x) + cos²(x) = 1) and other relationships like the angle addition formulas. This universality makes them integral to various branches of mathematics, including calculus and algebra, beyond just geometry.

In contrast to the other statements, which impose restrictions or limitations on the application of trigonometric identities, the correct statement accurately reflects their broad applicability and importance in mathematical analysis and problem-solving. Therefore, identifying that trigonometric identities are equalities involving trigonometric functions underscores their role as essential tools in various mathematical contexts.