91Ó°ÊÓ

Derive the formula \(\cos a=\cos b \cos c+\sin b \sin c \cos A\) for an arbitrary spherical triangle with sides \(a, b, c\) and op-posite angles \(A, B, C\) on a sphere of radius 1 by dividing the triangle into two right triangles and applying the formulas of Chapter 5 .

Show that a map with the minimal number of countries that requires at least five colors cannot contain a digon (a) country with only two boundary edges).