为什么sin(2A+π/3)+sin(2A-π/3)=sin2ART

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为什么sin(2A+π/3)+sin(2A-π/3)=sin2ART为什么sin(2A+π/3)+sin(2A-π/3)=sin2ART为什么sin(2A+π/3)+sin(2A-π/3)=sin2A

为什么sin(2A+π/3)+sin(2A-π/3)=sin2ART
为什么sin(2A+π/3)+sin(2A-π/3)=sin2A
RT

为什么sin(2A+π/3)+sin(2A-π/3)=sin2ART
左边=sin2Acosπ/3+cos2Asinπ/3+sin2Acosπ/3-cos2Asinπ/3
=2sin2Acosπ/3
=2sin2A*1/2
=sin2A=右边
命题得证

你把等号左面的部分全展开算

sin(2A+π/3)+sin(2A-π/3)=sin2Acos(π/3)+cos2Asin(π/3)+sin2Acos(π/3)-cos2Asin(π/3)=2sin2Acos(π/3)=sin2A