Question

Tan x * sec x / csc x * cot x =

Answer 1

D. tan x

Explanation:

Given the trigonometric expression:

`(\tan x \cdot \sec x)/(\csc x) \cdot \cot x`

Now, the expression can be rewritten in the form below:

`\begin{gathered} (\tan x\cdot\sec x)/(1)*(\cot x)/(\csc x)\frac{}{} \\ \begin{equation*} =\tan x*(\sec x)/(\csc x)\cdot\cot x \end{equation*} \\ =\frac{\sin(x)}{\cos(\text{x})}*(\cos x)/(\sin x)*(\sec x)/(\csc x)\text{ where }\begin{cases}\tan x=\frac{\sin x}{\cos\text{ x}} \\ \cot x=(cosx)/(sinx)\end{cases} \\ =(\sec x)/(\csc x) \\ =(1)/(\cos x)/(1)/(\sin x) \\ =(1)/(\cos x)*\sin x \\ =(\sin x)/(\cos x) \\ =\tan x \end{gathered}`

The expression is equivalent to tan x.

Option D is correct.