【紧急求助】计算:cosα+cos(2π/3 +α)+cos(4π/3 +α)

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【紧急求助】计算:cosα+cos(2π/3 +α)+cos(4π/3 +α)

【紧急求助】计算:cosα+cos(2π/3 +α)+cos(4π/3 +α)
【紧急求助】计算:cosα+cos(2π/3 +α)+cos(4π/3 +α)

【紧急求助】计算:cosα+cos(2π/3 +α)+cos(4π/3 +α)
=cosα+cos2π/3 *cosα-sin2π/3*sinα+cos4π/3*cosα-sin4π/3* sinα
=cosα-1/2cosα-(根号3)/2sinα-1/2cosα+(根号3)/2sinα
=0

=cosα+cos(2π/3)cosα-sin(2π/3)sinα+cos(4π/3)cosα-sin(4π/3)sinα
=cosα-1/2cosα+sin(4π/3)sinα-1/2cosα-sin(4π/3)sinα
=0