\[\operatorname{dn}(u+v)=\frac{\operatorname{cn}u\operatorname{dn}u\operatorname%
{cn}v\operatorname{dn}v+{k^{\prime}}^{2}\operatorname{sn}u\operatorname{sn}v}{%
\operatorname{cn}u\operatorname{cn}v+\operatorname{sn}u\operatorname{dn}u%
\operatorname{sn}v\operatorname{dn}v}.\]