球面三角法
tan  A + B 2 = cos  a − b 2 cos  a + b 2 cot  C 2 tan  A − B 2 = sin  a − b 2 sin  a + b 2 cot  C 2 tan  a + b 2 = cos  A − B 2 cos  A + B 2 tan  c 2 tan  a − b 2 = sin  A − B 2 sin  A + B 2 tan  c 2 {\displaystyle {\begin{aligned}\tan {\frac {A+B}{2}}={\frac {\cos {\dfrac {a-b}{2}}}{\cos {\dfrac {a+b}{2}}}}\cot {\frac {C}{2}}\\\tan {\frac {A-B}{2}}={\frac {\sin {\dfrac {a-b}{2}}}{\sin {\dfrac {a+b}{2}}}}\cot {\frac {C}{2}}\\\tan {\frac {a+b}{2}}={\frac {\cos {\dfrac {A-B}{2}}}{\cos {\dfrac {A+B}{2}}}}\tan {\frac {c}{2}}\\\tan {\frac {a-b}{2}}={\frac {\sin {\dfrac {A-B}{2}}}{\sin {\dfrac {A+B}{2}}}}\tan {\frac {c}{2}}\end{aligned}}}