Draw a spherical triangle on the surface of the unit sphere with center at the origin . Let the sides (arcs) opposite the vertices have lengths , and , and let be the angle at vertex . The spherical law of cosines is then given by , with two analogs obtained by permutations.

Let be the plane tangent to the sphere at , and let and . Then , , and . Express the length of in two ways using the usual planar law of cosines for the triangle in the plane :