Question

设a=

1

2

cos8°-

3

2

sin8°，b=

2tan13°

1-tan213°

，c=

1-cos52° 2

，则a，b，c的大小关系为______．

Answer 1

∵a=

1

2

cos8°-

3

2

sin8°=cos60°•cos8°-sin60°•sin8°=cos68°=sin22°，
b=

2tan13°

1-tan213°

=tan26°
c=

1-cos52° 2

=sin26°
∵sin22°＜sin26°＜tan26°
∴a＜c＜b
故答案为：a＜c＜b