作业帮将sinx+siny+sinz-sin(x+y+z)化为积的形式
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/03 12:59:37
将sinx+siny+sinz-sin(x+y+z)化为积的形式
将sinx+siny+sinz-sin(x+y+z)化为积的形式
将sinx+siny+sinz-sin(x+y+z)化为积的形式
sinx+siny+sinz-sin(x+y+z)
=2sin(x+y)/2cos(x-y)/2-2cos(x+y+2z)/2sin(x+y)/2
=2sin(x+y)/2[cos(x-y)/2-cos(x+y+2z)/2]
=2sin(x+y)/2*2sin(x+2z)/2sin(y+z)
=4sin(x+y)/2*sin(x+2z)/2*sin(y+z)
（希望能帮到你）
用积化和差公式cosαsinβ= 1/2[sin(α+β)-sin(α-β)]
sinx+siny=sinx+siny=sin[(x+y)/2+(x-y)/2]+sin[(x+y)/2-(x-y)/2]
=sin(x+y)/2cos(x-y)/2+cos(x+y)/2sin(x-y)/2+sin(x+y)/2cos(x-y)/2-cos(x+y)/2sin(x-y)/2
...
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用积化和差公式cosαsinβ= 1/2[sin(α+β)-sin(α-β)]
sinx+siny=sinx+siny=sin[(x+y)/2+(x-y)/2]+sin[(x+y)/2-(x-y)/2]
=sin(x+y)/2cos(x-y)/2+cos(x+y)/2sin(x-y)/2+sin(x+y)/2cos(x-y)/2-cos(x+y)/2sin(x-y)/2
=2sin(x+y)/2cos(x-y)/2
=2sin(x+y)/2cos(x-y)/2--2sin(x+y)/2--cos(x+y+2z)/2
=2sin(x+y)/2{cos(x-y)/2--cos(x+y+2z)/2}
=2sin(x+y)/22sin(y+z)sin(x+z)
=4sin[(x+y)/2]sin(y+z)/2sin(x+z)/2
收起
原式=2sin[(x+y)/2]cos[(x-y)/2]-2cos[(x+y+2z)/2]sin[(x+y)/2]
=2sin[(x+y)/2]【cos[(x-y)/2]-cos[(x+y+2z)/2]】
=2sin[(x+y)/2]×2sin[(x+2z)/2]sin(y+z)
=4sin[(x+y)/2]×sin[(x+2z)/2]×sin(y+z)
运用积化和差和差化积