Answer:
[tex]y=\text{tan}(x)[/tex] will have asymptote, when [tex]\text{cos}(x)=0[/tex].
Step-by-step explanation:
We are asked to find the asymptotes of the function [tex]y=\text{tan}(x)[/tex].
We can represent tangent as [tex]\text{tan}(x)=\frac{\text{sin}(x)}{\text{cos}(x)}[/tex].
We know that a rational function is undefined, when denominator is zero. So our function will have asymptote, when [tex]\text{cos}(x)=0[/tex].
We know that [tex]\text{cos}(x)=0[/tex] at [tex]\pm \frac{\pi}{2}+n[/tex].
