In Exercises 59–68, verify each identity. x sin x cot ------ = ----------------- 2 1 - cos x

Key Concepts

Trigonometric Identities

Trigonometric identities are equations that involve trigonometric functions and are true for all values of the variables involved. Common identities include the Pythagorean identities, reciprocal identities, and co-function identities. Understanding these identities is crucial for simplifying expressions and verifying equations in trigonometry.

Cotangent Function

The cotangent function, denoted as cot(x), is the reciprocal of the tangent function, defined as cot(x) = cos(x)/sin(x). It is important to understand how cotangent relates to sine and cosine, as this relationship is often used in trigonometric identities and simplifications. Recognizing how to manipulate these functions is key to solving problems involving cotangent.

Sine and Cosine Functions

Sine and cosine are fundamental trigonometric functions that relate the angles of a right triangle to the ratios of its sides. The sine function gives the ratio of the opposite side to the hypotenuse, while the cosine function gives the ratio of the adjacent side to the hypotenuse. Mastery of these functions is essential for working with trigonometric identities and solving equations involving angles.