A)Show that (sin B - cos B)^2 +(sin C - cos C)^2 - (sin A - cos A)^2
=1 - (sin2B+sin2C -sin2A).
B) If A+B+C=180,deduce, from A),that
(Sin B - cos B)^2 + (sin C - cos C)^2 - (sin A -cos A)^2
=1 - 4sinAcosBcosC.
Furthermore, if A = 90, find the greatest value of cosBcosC.