How do I find the vertical asymptotes of f(x)=tan2x?

Jun 26, 2018

Shown below

Explanation:

$y = \tan 2 x$

$y = \frac{\sin 2 x}{\cos 2 x}$

The vertical asymptote occurs when the function is undefined, in this case where the numerator is equal to 0 , as you can't divide by 0

$\cos 2 x = 0$

$\cos 2 x = \cos \left(\frac{\pi}{2}\right)$

$\implies 2 x = 2 \pi n \pm \frac{\pi}{2}$

=>color(red)( x = pi n pm pi/4

$\forall n \in \mathbb{Z}$