What is the reciprocal identity of tangent, tan(x)?

The reciprocal identity of tangent involves understanding the relationship between tangent and other trigonometric functions. Tangent is defined as the ratio of sine to cosine, which means that ( \tan(x) = \frac{\sin(x)}{\cos(x)} ).

The reciprocal of tangent is cotangent, denoted as ( \cot(x) ). Therefore, the reciprocal identity for tangent can be expressed as:

[

\tan(x) = \frac{1}{\cot(x)}

]

This shows that the correct representation of the reciprocal identity of tangent is indeed ( \frac{1}{\cot(x)} ).

This understanding is crucial in trigonometry, as it highlights the interrelated nature of the different functions, allowing for conversions and manipulations between them as needed in various mathematical contexts.