tan(2x) is undefined or discontiunuous for x=(pi/4)+-(pi/2)k where k is any integer
y = lnx has the domain x>0
so now considering
y=ln(tan(2x))
tan(2x)>0
true for
0 < x <pi/4
2pi/4 < x < 3pi/4
4pi/4 < x < 5pi/4
etc, this is where it is defined, NOT where it is NOT defined.
so It is
not defined for -pi/4 <= x <= 0
pi/4 <= x <= 2pi/4
3pi/4 <= x <= pi etc
I think this is
(pi/4) +- (pi/2*k) <= x <= (pi/2) +- (pi/2*k) Where k is an integer
I think that this is where the function is undefined.
I also plotted it using http://rechneronline.de/function-graphs/
I think that the graph supports my conclusion but I will admit that I havn't looked at it that hard.
y=ln(tan2x).JPG
+118654 
