设x是第二象限角,cos(x/2)+sin(x/2)=负根号5除以2,求sin(x/2)-cos(x/2)的值

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设x是第二象限角,cos(x/2)+sin(x/2)=负根号5除以2,求sin(x/2)-cos(x/2)的值设x是第二象限角,cos(x/2)+sin(x/2)=负根号5除以2,求sin(x/2)-

设x是第二象限角,cos(x/2)+sin(x/2)=负根号5除以2,求sin(x/2)-cos(x/2)的值
设x是第二象限角,cos(x/2)+sin(x/2)=负根号5除以2,求sin(x/2)-cos(x/2)的值

设x是第二象限角,cos(x/2)+sin(x/2)=负根号5除以2,求sin(x/2)-cos(x/2)的值
(cos(x/2)+sin(x/2))*(sin(x/2)-cos(x/2))=sinx/2平方-cosx/2平方=负cosx……剩下的我不用说了吧……

[cos(x/2)+sin(x/2)]²=cos²(x/2)+sin²(x/2)+2cos(x/2)sin(x/2)=1+2cos(x/2)sin(x/2)=5/4
推出:2cos(x/2)sin(x/2)=1/4
[sin(x/2)-cos(x/2)]²=cos²(x/2)+sin²(x/2)-2cos(x/2)sin(...

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[cos(x/2)+sin(x/2)]²=cos²(x/2)+sin²(x/2)+2cos(x/2)sin(x/2)=1+2cos(x/2)sin(x/2)=5/4
推出:2cos(x/2)sin(x/2)=1/4
[sin(x/2)-cos(x/2)]²=cos²(x/2)+sin²(x/2)-2cos(x/2)sin(x/2)=1-2cos(x/2)sin(x/2)=3/4
sin(x/2)-cos(x/2)=±√3/2
因为x是第二象限角,所以sinx>0,cosx<0.故sin(x/2)-cos(x/2)=√3/2(根号3除以2)

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