Spherical Law of Haversines

Theorem
Let $\triangle ABC$ be a spherical triangle on the surface of a sphere whose center is $O$.

Let the sides $a, b, c$ of $\triangle ABC$ be measured by the angles subtended at $O$, where $a, b, c$ are opposite $A, B, C$ respectively.

Then:


 * $\operatorname {hav} a = \map {\operatorname {hav} } {b - c} + \sin b \sin c \operatorname {hav} A$

where $\operatorname {hav}$ denotes haversine.