已知α是第三象限角,且f(α)=sin(?α?π)cos(5π?α)tan(2π?α)cos(π2?α)tan(?α?π).(1)化简f

2024-12-26 20:11:13
推荐回答(1个)
回答1:

(1)f(α)=

sin(?α?π)cos(5π?α)tan(2π?α)
cos(
π
2
?α)tan(?α?π)
=
sinα(?cosα)(?tanα)
sinα(?tanα)
=-cosα.---------(4分)
(2)∵tan(π-α)=-2,∴tanα=2.---------(5分)
∴sinα=2cosα
∴(2cosα)2+cos2α=1
cos2α=
1
5
.----------(6分)
∵α是第三象限角,∴cosα=?
5
5
,∴f(α)=
5
5
.----------(8分)
(3)∵cos(?420°)=cos420°=cos60°=
1
2

∴f(α)=-cosα=?
1
2
.------(12分)