1/2(cos2A-cos2B)=sin(A+B)sin(A-B)求证

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1/2(cos2A-cos2B)=sin(A+B)sin(A-B)求证

1/2(cos2A-cos2B)=sin(A+B)sin(A-B)求证
1/2(cos2A-cos2B)=sin(A+B)sin(A-B)求证

1/2(cos2A-cos2B)=sin(A+B)sin(A-B)求证
直接用和差化积公式:
1/2*(cos2B-cos2A)
=1/2*{-2sin[(2B+2A)/2]sin[(2B-2A)/2]}
=-sin(B+A)sin(B-A)
=sin(A+B)sin(A-B).

由“和差化积公式”得cos2a-cos2b=-2sin(a+b)sin(a-b)=2sin(a+b)sin(b-a).===>(cos2a-cos2b)/2=sin(a+b)sin(b-a).