= (sina) 2-(sinb) 2 (square difference formula)

= (1-cos2a)/2-(1-cos2b)/2 (double angle formula)

= 1/2*(cos2b-cos2a) (merged)

=1/2 * {cos [(a+b)-(a-b)]-cos [(a+b)+(a-b)]} (angle 2a=(a+b)+(a-b), 2b = (a+b).

= 1/2 * {[cos(a+b)cos(a-b)+sin(a+b)sin(a-b)]-[cos(a+b)cos(a-b)-sin(a+b)sin(a-b)

= 1/2*2sin(a+b)sin(a-b) (merged)

=sin(a+b)sin(a-b) (approximate fraction)

The first half of the equation you need is in the fourth line, and the back of your equation can be used as a formula.