化简:sin方A+sin方(A-π/3)+sin方(A+π/3)
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化简:sin方A+sin方(A-π/3)+sin方(A+π/3)
![化简:sin方A+sin方(A-π/3)+sin方(A+π/3)](/uploads/image/z/18785663-71-3.jpg?t=%E5%8C%96%E7%AE%80%EF%BC%9Asin%E6%96%B9A%2Bsin%E6%96%B9%28A-%CF%80%2F3%29%2Bsin%E6%96%B9%28A%2B%CF%80%2F3%29)
sin方A+sin方(A-π/3)+sin方(A+π/3)
=(1-cos2A)/2+(1-cos(2A-2π/3))/2+(1-cos(2A+2π/3))/2
=3/2-cos2A/2-[cos(2A-2π/3)+cos(2A+2π/3)]/2
=3/2-cos2A/2-cos2Acos4π/3
=3/2-cos2A/2+cos2A/2
=3/2
=(1-cos2A)/2+(1-cos(2A-2π/3))/2+(1-cos(2A+2π/3))/2
=3/2-cos2A/2-[cos(2A-2π/3)+cos(2A+2π/3)]/2
=3/2-cos2A/2-cos2Acos4π/3
=3/2-cos2A/2+cos2A/2
=3/2
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