cosa^2+cos(2π/3-a)^2+cosacos(2π/3-a)化简
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cosa^2+cos(2π/3-a)^2+cosacos(2π/3-a)化简
Rt,谢谢
Rt,谢谢
cos²a+cos²(2π/3-a)+cosacos(2π/3-a)
=[cosa+cos(2π/3-a)]²-cosacos(2π/3-a)
=[2cosπ/3cos(a-π/3)]²-1/2[cos2π/3+cos(2a-2π/3)]
=cos²(a-π/3)+1/4-1/2cos(2a-2π/3)
=cos²(a-π/3)+1/4-1/2[2cos²(a-π/3)-1]
=cos²(a-π/3)+1/4-cos²(a-π/3)+1/2
=3/4
=[cosa+cos(2π/3-a)]²-cosacos(2π/3-a)
=[2cosπ/3cos(a-π/3)]²-1/2[cos2π/3+cos(2a-2π/3)]
=cos²(a-π/3)+1/4-1/2cos(2a-2π/3)
=cos²(a-π/3)+1/4-1/2[2cos²(a-π/3)-1]
=cos²(a-π/3)+1/4-cos²(a-π/3)+1/2
=3/4
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