已知sin(α+
|
∵已知sin(α+
)+sinα=-π 3
,-4 3 5
<α<0,π 2
∴sinαcos
+cosαsinπ 3
+sinα=π 3
sinα+3 2
cosα=3 2
sin(α+3
)=-π 6
,4 3 5
sin(α+
)=-π 6
,又-4 5
<α+π 3
<π 6
,π 6
所以cos(α+
)=π 6
.3 5
∴cosα=cos[(α+
)-π 6
]=cos(α+π 6
)•cosπ 6
+sin(α+π 6
)•sinπ 6
=π 6
•3 5
+(-3 2
)•4 5
=1 2
,3
-43 10
故答案为
.3
-43 10