cos^2α+cos^2(α+π/3)-cosαcos(α+π/3)化简

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cos^2α+cos^2(α+π/3)-cosαcos(α+π/3)化简
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cos^2α+cos^2(α+π/3)-cosαcos(α+π/3)化简
cos^2α+cos^2(α+π/3)-cosαcos(α+π/3)化简

cos^2α+cos^2(α+π/3)-cosαcos(α+π/3)化简
cos²α+cos²(α+π/3)-cosαcos(α+π/3)
=1+[cos2α+cos2(α+π/3)]/2-cosαcos(α+π/3)
=1+cos(2α+π/3)cos(π/3)-[cos(2α+π/3)+cos(π/3)]/2
=1+[cos(2α+π/3)]/2-[cos(2α+π/3)]/2-1/4
=1-1/4
=3/4

原式=cosα+(-1/2)cosα+(√3/2)sinα+(-1/2)cosa-(√3/2)sinα
=0