球面三角法
2 s = a + b + c {\displaystyle 2s=a+b+c} 、 2 S = A + B + C {\displaystyle 2S=A+B+C} とおく。
sin  A 2 = sin  ( s − b ) sin  ( s − c ) sin  b sin  c cos  A 2 = sin  s sin  ( s − a ) sin  b sin  c tan  A 2 = sin  ( s − b ) sin  ( s − c ) sin  s sin  ( s − a ) {\displaystyle {\begin{aligned}\sin {\frac {A}{2}}&={\sqrt {\frac {\sin(s-b)\sin(s-c)}{\sin b\sin c}}}\\\cos {\frac {A}{2}}&={\sqrt {\frac {\sin s\sin(s-a)}{\sin b\sin c}}}\\\tan {\frac {A}{2}}&={\sqrt {\frac {\sin(s-b)\sin(s-c)}{\sin s\sin(s-a)}}}\end{aligned}}}