it can be explained easily by giving values for x;
let us give x=45
tan45+tan45=2
2tan45=2*1=2.
here it becomes eaual;
also assign another value x=30
tan30+tan30=1/(root3)+1/(root3)
=2/(root3)
2tan30=2/(root3);
so both assignation says the above equation is equal;
therefore tanx+tanx=2tanx