Answer with explanation:
we have to find the Asymptote of the function:
[tex]y=\cot(x-\frac{2\pi}{3})[/tex]
As period of cot x is equal to [-π, π].
[tex]x-\frac{2\pi}{3}=0\\\\x=\frac{2\pi}{3}\\\\ x-\frac{2\pi}{3}=\pi\\\\x=\frac{2\pi}{3}+\pi \\\\x=\frac{5\pi}{3} \\\\x=\cot(2\pi -\frac{\pi}{3})\\\\x=\frac{-\pi}{3}[/tex]
You can find asymptote by drawing the graph of
[tex]y=\cot(x-\frac{2\pi}{3})[/tex]
There are two Asymptotes
[tex]1.\rightarrow x= \frac{-\pi}{3}\\\\2..\rightarrow x= \frac{2\pi}{3}[/tex]
Out of the four option
⇒Option B
[tex]x=\frac{-\pi}{3}[/tex] is one asymptote of the graph.
