sin (A+B).sin(A-B)=
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sin(A+B).sin(A−B)
=[sin(A)cos(B)+cos(A)sin(B)][sin(A)cos(B)−cos(A)sin(B)]
=sin2Acos2A−cos2Asin2A
=sin2A[1−sin2B]−[1−sin2A]sin2B
=sin2A−sin2Asin2B−sin2B+sin2Asin2B
=sin2A−sin2B
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