化简cos[(3k+1)π/3+α]+cos[(3k-1)π/3-α],其中k∈Z请给比较详细的过程,我比较笨~(@^_^@)~

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化简cos[(3k+1)π/3+α]+cos[(3k-1)π/3-α],其中k∈Z请给比较详细的过程,我比较笨~(@^_^@)~
化简cos[(3k+1)π/3+α]+cos[(3k-1)π/3-α],其中k∈Z
请给比较详细的过程,我比较笨~(@^_^@)~

化简cos[(3k+1)π/3+α]+cos[(3k-1)π/3-α],其中k∈Z请给比较详细的过程,我比较笨~(@^_^@)~
cos( kπ+π/3+a)+cos(kπ-π/3-a)
当k=2n 时:原式=cos(π/3+a)+cos(π/3+a)=2cos(π/3+a)
当k=2n+1时:原式=-cos(π/3+a)-cos(π/3+a)=-2cos(π/3+a)


cos[(3k+1)/3 *π + α]+cos[(3k-1)/3 *π – α]
= cos(kπ+π/3 +α)+cos(kπ-π/3 -α)
=[cos(kπ)cos(π/3+α)-sin(kπ)sin(π/3+α)]+[cos(kπ)cos(π/3+α)+sin(kπ)sin(π/3+α)]
=2cos(kπ)cos(π/3+α)
[1]当k=2n...

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cos[(3k+1)/3 *π + α]+cos[(3k-1)/3 *π – α]
= cos(kπ+π/3 +α)+cos(kπ-π/3 -α)
=[cos(kπ)cos(π/3+α)-sin(kπ)sin(π/3+α)]+[cos(kπ)cos(π/3+α)+sin(kπ)sin(π/3+α)]
=2cos(kπ)cos(π/3+α)
[1]当k=2n,n∈Z时,
cos[(3k+1)/3*π + α]+cos[(3k-1)/3 * π – α]
=2cos(kπ)cos(π/3 + α)
=2cos(π/3 + α)
=cosα-√3sinα
[2]当k=2n+1,n∈Z时,
cos[(3k+1)/3 *π + α]+cos[(3k-1)/3 * π – α]
=2cos(kπ)cos(π/3 + α)
=-2cos(π/3 + α)
=-cosα+√3sinα

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