已知a∈(π2,π),sina=35,则tan(a-π4)等于()A.-7B.-17C.7D.17-数学

题目简介

已知a∈(π2,π),sina=35,则tan(a-π4)等于()A.-7B.-17C.7D.17-数学

题目详情

已知a∈(
π
2
,π),sina=
3
5
,则tan(a-
π
4
)等于(  )
A.-7B.-
1
7
C.7D.
1
7
题型:单选题难度:中档来源:宝山区二模

答案

∵a∈(class="stub"π
2
,π),sina=class="stub"3
5

∴cosa=-class="stub"4
5
,则tana=class="stub"sina
cosa
=
class="stub"3
5
-class="stub"4
5
=-class="stub"3
4

∴tan(a-class="stub"π
4
)=
tana-tanclass="stub"π
4
1+tanatanclass="stub"π
4
=
-class="stub"3
4
-1
1+(-class="stub"3
4
)×1
=-7
故选A.

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