How do I find the vertical asymptotes of $f (x) = tan 2 x$ $f(x)=tan2x$ ?

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Answer 1 · 2018-06-26T21:09:16

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$y = tan 2 x$ $y = tan2x$

$y = \frac{sin 2 x}{cos 2 x}$ $y = (sin2x)/(cos2x)$

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

$cos 2 x = 0$ $cos2x = 0$

$cos 2 x = cos (\frac{π}{2})$ $cos2x = cos (pi/2)$

$\Rightarrow 2 x = 2 π n \pm \frac{π}{2}$ $=> 2x = 2pi n pm pi/2$

$\Rightarrow x = π n \pm \frac{π}{4}$ $=>color(red)( x = pi n pm pi/4$

$AAn in ZZ$

How do I find the vertical asymptotes of f(x)=tan2xf(x)=tan2xf(x)=tan2x?