Answer:
the asymptotes of graph y=tan(x) occur at [tex]\frac{pi}{2}+n\pi[/tex]
Step-by-step explanation:
The graph of y=tan(x) is shown in figure-1
[tex]tan\,x=\frac{sin\,x}{cos\,x}[/tex]
so, the vertical asymptotes occur when dinominator is zero
cos x = 0
[tex]0=cos(\frac{pi}{2}) = cos(\frac{pi}{2}+n\pi)[/tex]
The vertical asymptotes occur at x=[tex]\frac{pi}{2}+n\pi[/tex]
where n is an integer.
Hence, the asymptotes of graph y=tan(x) occur at [tex]\frac{pi}{2}+n\pi[/tex]
