已知tan(α−π6)=37,tan(π6+β)=25,则tan(α+β)的值为( ) A.2941 B.129 C.141 D.1
问题描述:
已知tan(α−
)=π 6
,tan(3 7
+β)=π 6
,则tan(α+β)的值为( )2 5
A.
29 41
B.
1 29
C.
1 41
D. 1
答
tan(α+β)=tan[(α-
)+(π 6
+β)]=π 6
=tan(α−
)+(π 6
+β)π 6 1−tan(α−
)•tan(π 6
+β)π 6
=1,
+3 7
2 5 1−
× 3 7
2 5
故选D.