Question

设a=

1

2

cos60-

3

2

sin60，b=

2tan130

1+tan2130

，c=

1-cos500 2

，则a，b，c按从小到大的顺序排列为______．

Answer 1

a=

1

2

cos60-

3

2

sin60=cos(60° +6°)=cos54°
b=

2tan130

1+tan2130

=

2sin13° cos13°

1+ sin213° cos213

=

2sin13°cos13°

1

=sin26°=cos74°
c=

1-cos500 2 cos225

=cos25
因为y=cosx在[0，

π

2

]上单调递减，所以b＜a＜c
故选B＜a＜c