中四數學問題 PROOF~

L.H.S.
= sin(A+B) sin(A -B)
= - (1/2) [ cos(A+B + A-B) - cos(A+B - (A-B)) ]
= - (1/2) ( cos2A - cos2B )
= - (1/2) ( 1 - 2sin²A - (1 - 2sin²B) )
= - (1/2) ( 2sin²B - 2sin²A )
= sin²A - sin²B
= R.H.S.

2012-08-09 14:01:10 補充：
Method 2 :

sin(A+B) sin(A -B)
= (sinA cosB + cosA sinB) (sinA cosB - cosA sinB)
= sin²A cos²B - cos²A sin²B
= sin²A (1 - sin²B) - (1 - sin²A) sin²B
= sin²A - sin²B