已知tan(α+β)=
|
∵tan(α+β)=
,tan(β-2 5
)=π 3
,1 4
∴tan(α+
)=tan[(α+β)-(β-π 3
)]=π 3
=
-2 5 1 4 1+
×2 5 1 4
,3 22
则tan(
-α)=tan[π 6
-(α+π 2
)]=cot(α+π 3
)=π 3
=1 tan(α+
)π 3
.22 3
故答案为:22 3
已知tan(α+β)=
|
∵tan(α+β)=
,tan(β-2 5
)=π 3
,1 4
∴tan(α+
)=tan[(α+β)-(β-π 3
)]=π 3
=
-2 5 1 4 1+
×2 5 1 4
,3 22
则tan(
-α)=tan[π 6
-(α+π 2
)]=cot(α+π 3
)=π 3
=1 tan(α+
)π 3
.22 3
故答案为:22 3