How do you prove that tangent is an odd function?

1 Answer
Jan 30, 2015

A function is even if:

f(-x)=f(x)f(x)=f(x).

A function is odd if:

f(-x)=-f(x)f(x)=f(x).

In this case:
y=tan(-x)=sin(-x)/cos(-x)=(-sin(x))/cosx=-sinx/cosx=-tan(x)y=tan(x)=sin(x)cos(x)=sin(x)cosx=sinxcosx=tan(x),

for the simmetry of sinus and cosinus.