化简 sin(π+α)+sin(2π+α)+sin(3π+α)+……+sin(kπ+α) k属于Z

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化简sin(π+α)+sin(2π+α)+sin(3π+α)+……+sin(kπ+α)k属于Z化简sin(π+α)+sin(2π+α)+sin(3π+α)+……+sin(kπ+α)k属于Z化简sin(

化简 sin(π+α)+sin(2π+α)+sin(3π+α)+……+sin(kπ+α) k属于Z
化简 sin(π+α)+sin(2π+α)+sin(3π+α)+……+sin(kπ+α) k属于Z

化简 sin(π+α)+sin(2π+α)+sin(3π+α)+……+sin(kπ+α) k属于Z
sin(π+α)=-sina
sina=sin(2π+α)=sin(4π+α).
sin(π+α)+sin(2π+α)+sin(3π+α)+……+sin(kπ+α)
所以当k=2n时,k为偶数时
原式=-sina+sina-sina+sina.
=0
当k=2n+1时即k为奇数时
原式=-sina+sina-sina+sina.
=-sina
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