How is cot(x) expressed in terms of tan(x)?

The correct expression for cot(x) in terms of tan(x) is indeed 1/tan(x). To understand why this is the case, it helps to recall the definitions of the trigonometric functions involved.

Cotangent (cot) is defined as the ratio of the cosine function to the sine function:

[

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

]

Tangent (tan), on the other hand, is defined as the ratio of sine to cosine:

[

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

]

If we take the reciprocal of the tangent function, we express cotangent in terms of tangent:

[

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

]

This shows that cotangent is indeed the reciprocal of tangent. Thus, representing cot(x) as 1/tan(x) is accurate and aligns with the fundamental properties of these trigonometric functions.

The other choices do not accurately express cotangent in terms of tangent, as they involve combinations or ratios of sine and cosine without the correct relationship to tangent. Hence, the expression 1/tan(x) is the valid relationship, reinforcing the definitions of cotangent