Question

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

Answer 1

`tanx = sinx/cosx`
domain is all the values that x can take such that y always exists and is finite for that value of x.
thus x can take all such values where `cosx` is not zero because if `cosx` will be zero
`tanx` will become infinity and hence not defined .
thus domain is : all real numbers except the numbers at which `cosx` is zero i.e. `npi/2` where n= 1,3,5,.........

range of `tanx` is all real numbers as it can take any value .