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. )