How do you prove that tangent is an odd function?

A function is even if:
##f(-x)=f(x)##.
A function is odd if:
##f(-x)=-f(x)##.
In this case:
##y=tan(-x)=sin(-x)/cos(-x)=(-sin(x))/cosx=-sinx/cosx=-tan(x)##
for the simmetry of sinus and cosinus.