What is the reciprocal identity of cotangent, cot(x)?

The reciprocal identity for the cotangent function states that cotangent is the reciprocal of the tangent function. Specifically, the cotangent of an angle ( x ) can be defined as:

[

\cot(x) = \frac{\cos(x)}{\sin(x)}

]

From this definition, it follows that if you take the reciprocal of ( \cot(x) ), you can write:

[

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

]

This reveals that cotangent's reciprocal is indeed tangent, which is directly reflected in the relationship stated in the answer option. Hence, the reciprocal of ( \cot(x) ) is expressed mathematically as ( \cot(x)^{-1} = \tan(x) ).

Since the correct answer states that the reciprocal identity of cotangent ( \cot(x) ) is ( 1/\tan(x) ), it aligns with this established property. Thus, recognizing that ( \frac{1}{\tan(x)} = \cot(x) ) validates this response as accurate and demonstrates a fundamental concept in trigonometric identities.