\[\operatorname{cd}(u+v)=\frac{\operatorname{cd}u\operatorname{cd}v-{k^{\prime}}%
^{2}\operatorname{sd}u\operatorname{nd}u\operatorname{sd}v\operatorname{nd}v}{%
1+k^{2}{k^{\prime}}^{2}{\operatorname{sd}}^{2}u{\operatorname{sd}}^{2}v},\]