The square of cosa = the square of COSB+A,

Sina's square = 1-cosb's square-a.

(2) Two-angle sum formula

sin(A+B) = sinAcosB+cosAsinB，

sin(A-B) = sinAcosB-cosAsinB .

So sin (a+b) sin (a-b) = square of Sina, square of cosB-square of -cosA, square of sinB.

= (1-square of cosb-a) square of cosb-(square of cosb+a) (1-square of cosb)

=-a (note: simple expansion. )