已知0<α<π2<β<π,sinα=35,sinβ=45.(1)求cosβ;(2)求tan(α+β).-数学

题目简介

已知0<α<π2<β<π,sinα=35,sinβ=45.(1)求cosβ;(2)求tan(α+β).-数学

题目详情

已知0<α<
π
2
<β<π,sinα=
3
5
,sinβ=
4
5

(1)求cosβ;    
(2)求tan(α+β).
题型:解答题难度:中档来源:不详

答案

(1)∵sinβ=class="stub"4
5
class="stub"π
2
<β<π

又∵sin2β+cos2β=1
∴cosβ=-class="stub"3
5

(2)∵sinα=class="stub"3
5
0<α<class="stub"π
2
,sin2α+cos2α=1
cosα=class="stub"4
5
tanα=class="stub"3
4

又∵tanβ=-class="stub"4
3

tan(α+β)=class="stub"tanα+tanβ
1-tanαtanβ
=
class="stub"3
4
+(-class="stub"4
3
)
1-class="stub"3
4
×(-class="stub"4
3
)
=-class="stub"7
25
(10分)

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