To simplify the expression 1/tan(x), we can start by recalling the definition of the tangent function in terms of sine and cosine. The tangent of an angle x is defined as:
tan(x) = sin(x) / cos(x)
So, if we want to simplify 1/tan(x), we can substitute this definition into our expression:
1/tan(x) = 1/(sin(x)/cos(x))
Next, dividing by a fraction is the same as multiplying by its reciprocal. Therefore, we rewrite the expression as:
1/tan(x) = cos(x)/sin(x)
The result, cos(x)/sin(x), is another trigonometric function known as cotangent. Thus, we can express our simplified form in terms of cotangent:
1/tan(x) = cot(x)
In summary, the expression 1/tan(x) simplifies to cot(x). This relationship holds for any value of x where tan(x) is defined (i.e., where cosine is not zero).