已知sin(α+β)=23,tanαtanβ=713,则sin(α-β)=______.-数学

题目简介

已知sin(α+β)=23,tanαtanβ=713,则sin(α-β)=______.-数学

题目详情

已知sin(α+β)=
2
3
tanα
tanβ
=
7
13
,则sin(α-β)=______.
题型:填空题难度:中档来源:不详

答案

∵sin(α+β)=sinαcosβ+cosαsinβ=class="stub"2
3
,sin(α-β)=sinαcosβ-cosαsinβ,
class="stub"tanα
tanβ
=class="stub"7
13

sin(α+β)
sin(α-β)
=class="stub"sinαcosβ+cosαsinβ
sinαcosβ-cosαsinβ
=class="stub"tanα+tanβ
tanα-tanβ
=
class="stub"tanα
tanβ
+1
class="stub"tanα
tanβ
-1
,即
class="stub"2
3
sin(α-β)
=
class="stub"7
13
+1
class="stub"7
13
-1

解得sin(α-β)=-class="stub"1
5

故答案为:-class="stub"1
5

更多内容推荐