Perform the indicated operation and simplify the result. \[ \cot x(\tan x-\sec x) \] The answer is

Step 1 ：Rewrite the expression as follows: \(\frac{1}{\tan x}(\tan x - \frac{1}{\cos x})\)

Step 2 ：Distribute the cotangent of x to both terms inside the parentheses: \(\frac{1}{\tan x} \cdot \tan x - \frac{1}{\tan x} \cdot \frac{1}{\cos x}\)

Step 3 ：Simplify the first term to 1, and the second term to the cotangent of x divided by the cosine of x: \(1 - \frac{\cot x}{\cos x}\)

Step 4 ：Simplify the expression to 1 - 1/sin(x), which is the same as 1 - csc(x)

Step 5 ：Final Answer: \(\boxed{1 - \csc x}\)