化简 cos(3k+1π/3 +X)+cos(3k-1π/3-X)其中k属于整数

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化简 cos(3k+1π/3 +X)+cos(3k-1π/3-X)其中k属于整数

化简 cos(3k+1π/3 +X)+cos(3k-1π/3-X)其中k属于整数
化简 cos(3k+1π/3 +X)+cos(3k-1π/3-X)其中k属于整数

化简 cos(3k+1π/3 +X)+cos(3k-1π/3-X)其中k属于整数
cos[(3k+1)π/3+x]+cos[(3k-1)π/3-x]
= 2 cos½[(3k+1)π/3+x+(3k-1)π/3-x] * cos½[(3k+1)π/3+x-(3k-1)π/3+x]
= 2 coskπ * cos(x+π/3)
= coskπ * (cosx - √3 sinx)
k 为偶数时,原式 = cosx - √3 sinx
k 为奇数时,原式 = - cosx + √3 sinx

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