\[\operatorname{dn}(u+v)=\frac{\operatorname{sn}u\operatorname{cn}v\operatorname%
{dn}u-\operatorname{sn}v\operatorname{cn}u\operatorname{dn}v}{\operatorname{sn%
}u\operatorname{cn}v\operatorname{dn}v-\operatorname{sn}v\operatorname{cn}u%
\operatorname{dn}u},\]