tanx/tan3x
=I1−3tan^2x)/(3−tan^2x)_
=3(3−tan^2x)−8)/(3−tan^2x)
=(1-3tan^2x)/(3−tan^2x)
Now let z = tanx
f(z)=(1-3z^2/(3-z^2)
so it looks like z cannot be sqrt(3), or
tan x cannot be sqrt3, or x cannot be....
Find domain of tanx/tan3x
2 answers
the function is undefined where the denominator is zero. That is,
tan(3x) = 0
this occurs when 3x = nπ
or, x = n * π/3
where x=nπ the function is 0/0, so there are holes there.
the function is also undefined when the numerator or denominator is undefined. That is, when
3x or x is an odd multiple of π/2
If you look at the graph, all you see are the asymptotes, but the holes are also excluded from the domain.
tan(3x) = 0
this occurs when 3x = nπ
or, x = n * π/3
where x=nπ the function is 0/0, so there are holes there.
the function is also undefined when the numerator or denominator is undefined. That is, when
3x or x is an odd multiple of π/2
If you look at the graph, all you see are the asymptotes, but the holes are also excluded from the domain.