Reciprocal identities are fundamental relationships in trigonometry that express the relationships between the six trigonometric functions. They show how each function can be defined in terms of its reciprocal. The primary reciprocal identities are: csc(θ) = 1/sin(θ), sec(θ) = 1/cos(θ), and cot(θ) = 1/tan(θ). These identities are useful for simplifying trigonometric expressions and solving equations. By using reciprocal identities, one can easily switch between different trigonometric functions, making it easier to analyze and understand various mathematical problems involving angles and triangles.