# How do you find the domain and range of y=tan x?

$\tan x = \sin \frac{x}{\cos} x$
thus x can take all such values where $\cos x$ is not zero because if $\cos x$ will be zero
$\tan x$ will become infinity and hence not defined .
thus domain is : all real numbers except the numbers at which $\cos x$ is zero i.e. $n \frac{\pi}{2}$ where n= 1,3,5,.........
range of $\tan x$ is all real numbers as it can take any value .