Verify the Identity

Question

Sin(u+v)/cos(u)cos(v)=tan(u)+tan(v)

 

I need help with this, I'm supposed to solve one side until it looks like the other. 

Answer 1

tanu + tanv = sinu/cosu + sinv/cosv

 

                  = [sinucosv + cosusinv] / (cosucosv)

 

                  = sin(u+v) / (cosucosv)

Answer 2

Sin(u+v)/cos(u)cos(v)=(sin(u)cos(v)+sin(v)cos(u))/cos(u)cos(v)=

=sin(u)cos(v)/cos(u)cos(v)+sin(v)cos(u)/cos(u)cos(v)=

=sin(u)/cos(u)+sin(v)/cos(v)=tan(u)+tan(v)