sin(A) * sin(B) = 1/2 * cos(A-B) - 1/2 * cos(A+B) cos(A) * cos(B) = 1/2 * cos(A-B) + 1/2 * cos(A+B) sin(A) * cos(B) = 1/2 * sin(A-B) + 1/2 * sin(A+B) sin^2(A) + cos^2(B) = 1 cos(0) = 1