Half-side formula

These are formulae used in spherical trigonometry to solve spherical triangles.

$tan(a/2)=Rcos(S-\%alpha)$ $tan(b/2)=Rcos(S-\%beta)$ $tann(c/2)=Rcos(S-\%gamma)$

where $\%alpha,\%beta,\%gamma$ are the angles spherical triangle and $a,b,c$ are the lengths of the sides, a being opposite $\%alpha$ etc.and S is half the sum of the angles $S=1/2(\%alpha+\%beta+\%gamma)$ and $R={\frac {-cosS}{cos(S-\%alpha)cos(S-\%beta)cos(S_{\%}gamma)}}$