# What is the domain of tan(2x)?

$x \ne \frac{\pi}{4} + k \frac{\pi}{2}$.
The domain of the function $y = \tan f \left(x\right)$ is $f \left(x\right) \ne \frac{\pi}{2} + k \pi$, so:
$2 x \ne \frac{\pi}{2} + k \pi \Rightarrow x \ne \frac{\pi}{4} + k \frac{\pi}{2}$.