已知sin(π-α)-cos(π+α)=23(π2<α<π),则sinα-cosα=______.-数学

题目简介

已知sin(π-α)-cos(π+α)=23(π2<α<π),则sinα-cosα=______.-数学

题目详情

已知sin(π-α)-cos(π+α)=
2
3
π
2
<α<π
),则sinα-cosα=______.
题型:填空题难度:中档来源:不详

答案

sin(π-α)-cos(π+α)=sinα+cosα=
2
3
,所以sin2α+2sinαcosα+cos2α=class="stub"2
9
,-2sinαcosα=class="stub"7
9

(sinα-cosα)2=class="stub"16
9
,因为class="stub"π
2
<α<π
,所以sinα-cosα=class="stub"4
3

故答案为:class="stub"4
3

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