问题
填空题
已知tan(α+β)=
|
答案
∵tan(α+β)=
,tan(β-1 2
)=π 4
,∴tan(α+1 3
)=tan[(α+β)-(β-π 4
)]=π 4
=tan(α+β)-tan(β-
)π 4 1+tan(α+β)tan(β-
)π 4
=
-1 2 1 3 1+
×1 2 1 3
.1 7
∴tanα=tan(α+
-π 4
)=π 4
=tan(α+
)-tanπ 4 π 4 1+tan(α+
)tanπ 4 π 4
=-
-11 7 1+ 1 7
.3 4
∴sin(
+α)•sin(π 4
-α)=π 4
(cosα+sinα)•2 2
(cosα-sinα)=2 2
(cos2α-sin2α)=1 2
×1 2
=cos2α-sin2α cos2α+sin2α
×1 2
=1-tan2α 1+tan2α
×1 2
=1-(-
)23 4 1+(-
)23 4
.7 50
故答案为
.7 50