Answer:
The correct answer is "Option C".
Step-by-step explanation:
Given:
[tex]\bold{ 1) y= -\tan (x- \frac{\pi}{2})}\\\\\bold{ 2) y= \tan (x+ \frac{\pi}{2})}\\\\\bold{ 3) y= -\cot (x- \frac{\pi}{2})}\\\\\bold{ 4) y= \cot (x+ \frac{\pi}{2})}\\\\[/tex]
solve the above equation:
[tex]\Rightarrow 1) \ y= -\tan (x- \frac{\pi}{2})\\\\\Rightarrow \ y= \tan (\frac{\pi}{2}-x)\\\\\Rightarrow \ y= \cot x \ \ \ \ \ \bold{ that \ matchs \ graph \ D}\\\\ \Rightarrow 2) \ y= \tan (x+ \frac{\pi}{2})\\\\\Rightarrow \ y= - \cot x \ \ \ \ \bold{ that \ matchs \ graph \ A}\\\\[/tex]
[tex]\Rightarrow 3) \ y= -\cot (x- \frac{\pi}{2})\\\\\Rightarrow \ y=\cot ( \frac{\pi}{2}-x)\\\\\Rightarrow \ y=\tan x\ \ \ \ \bold{that \ matchs \ graph \ C}\\\\[/tex]
[tex]\Rightarrow 4) \ y= \cot (x+ \frac{\pi}{2})\\\\\Rightarrow \ y= \cot (\frac{\pi}{2}+x)\\\\\Rightarrow \ y= \ -tan x \ \ \ \ \ \bold{ that \ matchs \ graph \ A}[/tex]
The final answer is "Option C".
