\[\operatorname{cn}(u+v)=\frac{1-{\operatorname{sn}}^{2}u-{\operatorname{sn}}^{2%
}v+k^{2}{\operatorname{sn}}^{2}u{\operatorname{sn}}^{2}v}{\operatorname{cn}u%
\operatorname{cn}v+\operatorname{sn}u\operatorname{dn}u\operatorname{sn}v%
\operatorname{dn}v},\]