设a=cos61°?cos127°+cos29°?cos37°,b=2tan13°1+tan213°,c=1?cos50°2,则a,b,c的大小关系(由

2025-06-26 23:38:42
推荐回答(1个)
回答1:

cos61°?cos127°+cos29°?cos37°=-sin29°?sin37°+cos29°?cos37°=cos(37°+29°)=cos66°,即a=cos66°=sin24°,

2tan?13?
1+tan?213?
2
sin?13?
cos?13?
sin?13?+cos?13?
cos?213?
=2sin?13?cos?13?=sin?26?
1?cos50°
2
=
1?1+2sin225°
2
=
sin225°
=sin25°

∵sin24°<sin25°<sin26°,
∴a<c<b,
故答案为:a<c<b.