问题 选择题
cos(75°+α)=
1
3
,180°<α<270°
,则cos(105°-α)+sin(α-105°)=(  )
A.
1+2
2
3
B.
1-2
2
3
C.
-1-2
2
3
D.
-1+2
2
3
答案

∵cos(75°+α)=

1
3
,180°<α<270°,

∴255°<α+75°<345°,

∴sin(75°+α)=-

2
2
3

则cos(105°-α)+sin(α-105°)

=cos[180°-(75°+α)]+sin[(75°+α)-180°]

=-cos(75°+α)-sin(75°+α)

=-

1
3
+
2
2
3

=

-1+2
2
3

故选D

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