如何证明sin(A-B)*sin(A+B)=sinA²-sinB²

来源：学生作业帮助网编辑：作业帮时间：2024/04/28 10:50:33

如何证明sin(A-B)*sin(A+B)=sinA²-sinB²
如何证明sin(A-B)*sin(A+B)=sinA²-sinB²

如何证明sin(A-B)*sin(A+B)=sinA²-sinB²
左边用积化和差公式=(cos2B-cos2A)/2=(1-2sinB^2-1+2sinA^2)/2=sinA^2-sinB^2

sin(A-B)*sin(A+B)
=(sinAcosB-sinBcosA)*(sinAcosB+sinBcosA)
=sinA²cosB²-sinB²cosA²
=sinA²(1-sinB²)-sinB²(1-sinA²)
=sinA²-sinB²

sina(A-B)*sin(A+B)=[cos(A+B-A+B）-cos(A+B+A-B)]/2
=（cos2B-cos2A)/2=[1-2sinB*sinB-1+2sinA*sinA]/2
=sinA*sinA-sinB*sinB

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