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The expression for cotangent, denoted as cot(x), is defined as the ratio of the cosine function to the sine function. In mathematical terms, cot(x) = cos(x)/sin(x). This relationship arises from the definitions of the trigonometric functions in a right triangle context, where cotangent represents the adjacent side over the opposite side.

This definition highlights the reciprocal nature of cotangent in relation to tangent, since tangent is defined as tan(x) = sin(x)/cos(x). Consequently, cotangent can also be expressed as the reciprocal of tangent: cot(x) = 1/tan(x), which aligns with another identity.

Though there are other expressions related to cotangent, the most straightforward and common definition is the ratio of cosine to sine. Understanding this definition is fundamental for solving various problems in trigonometry, as it connects cotangent with the primary trigonometric functions and lays the groundwork for further explorations in identities and equations.