(1)f(α)=
=sin(?α?π)cos(5π?α)tan(2π?α) cos(
?α)tan(?α?π)π 2
=-cosα.---------(4分)sinα(?cosα)(?tanα) sinα(?tanα)
(2)∵tan(π-α)=-2,∴tanα=2.---------(5分)
.----------(6分)
∴sinα=2cosα ∴(2cosα)2+cos2α=1 cos2α=
1 5
∵α是第三象限角,∴cosα=?
,∴f(α)=
5
5
.----------(8分)
5
5
(3)∵cos(?420°)=cos420°=cos60°=
,1 2
∴f(α)=-cosα=?
.------(12分)1 2