Answer:
D. tan x
Explanation:
Given the trigonometric expression:
[tex]\frac{\tan x \cdot \sec x}{\csc x} \cdot \cot x[/tex]Now, the expression can be rewritten in the form below:
[tex]\begin{gathered} \frac{\tan x\cdot\sec x}{1}\times\frac{\cot x}{\csc x}\frac{}{} \\ \begin{equation*} =\tan x\times\frac{\sec x}{\csc x}\cdot\cot x \end{equation*} \\ =\frac{\sin(x)}{\cos(\text{x})}\times\frac{\cos x}{\sin x}\times\frac{\sec x}{\csc x}\text{ where }\begin{cases}\tan x=\frac{\sin x}{\cos\text{ x}} \\ \cot x=\frac{cosx}{sinx}\end{cases} \\ =\frac{\sec x}{\csc x} \\ =\frac{1}{\cos x}\div\frac{1}{\sin x} \\ =\frac{1}{\cos x}\times\sin x \\ =\frac{\sin x}{\cos x} \\ =\tan x \end{gathered}[/tex]The expression is equivalent to tan x.
Option D is correct.