Perform the indicated operation and simplify the result. $\tan x(\csc x-\cot x)$
The answer is

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Answer

So, the final answer is $\boxed{-1 + \sec x}$.

Steps

Step 1 ：Given the expression is $\tan x(\csc x-\cot x)$.

Step 2 ：We know that $\csc x = \frac{1}{\sin x}$, $\cot x = \frac{\cos x}{\sin x}$ and $\tan x = \frac{\sin x}{\cos x}$.

Step 3 ：Substitute these values into the expression to get $(-\frac{\cos x}{\sin x} + \frac{1}{\sin x})\frac{\sin x}{\cos x}$.

Step 4 ：Simplify the expression to get $-1 + \frac{1}{\cos x}$.

Step 5 ：This is equivalent to $-1 + \sec x$.

Step 6 ：So, the final answer is $\boxed{-1 + \sec x}$.