若cosxcosy+sinxsiny=12,sin2x+sin2y=23,则sin(x+y)=______.-数学

题目简介

若cosxcosy+sinxsiny=12,sin2x+sin2y=23,则sin(x+y)=______.-数学

题目详情

若cosxcosy+sinxsiny=
1
2
,sin2x+sin2y=
2
3
,则sin(x+y)=______.
题型:填空题难度:偏易来源:上海

答案

∵cosxcosy+sinxsiny=class="stub"1
2
,∴cos(x-y)=class="stub"1
2

∵sin2x+sin2y=class="stub"2
3
,∴2sin(x+y)cos(x-y)=class="stub"2
3

2sin(x+y)×class="stub"1
2
=class="stub"2
3

∴sin(x+y)=class="stub"2
3

故答案为class="stub"2
3

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