设x是第二象限角,且满足cos(x/2)+sin(x/2)=-(√5)/2,求sin(x/2)-cos(x/2)的值是多少

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设x是第二象限角,且满足cos(x/2)+sin(x/2)=-(√5)/2,求sin(x/2)-cos(x/2)的值是多少设x是第二象限角,且满足cos(x/2)+sin(x/2)=-(√5)/2,求

设x是第二象限角,且满足cos(x/2)+sin(x/2)=-(√5)/2,求sin(x/2)-cos(x/2)的值是多少
设x是第二象限角,且满足cos(x/2)+sin(x/2)=-(√5)/2,求sin(x/2)-cos(x/2)的值是多少

设x是第二象限角,且满足cos(x/2)+sin(x/2)=-(√5)/2,求sin(x/2)-cos(x/2)的值是多少
令后者=a前者加后者可得sin(x/2),前者减后者可得cos(x/2),然后取平方相加等于1,可算出答案

(cos(x/2)+sin(x/2))^2=1+2cos(x/2)sin(x/2)=5/4
2cos(x/2)sin(x/2)=1/4
(sin(x/2)-cos(x/2))^2=1-2cos(x/2)sin(x/2)=3/4
sin(x/2)-cos(x/2)=√3/2

10分之3倍的根下5

cos(x/2)+sin(x/2)=-(√5)/2说明|cos(x/2)|>|sin(x/2)|,而sin(x/2)>0,cos(x/2)<0,故所求值是负的