a=sin14°+cos14°=√2(cos45°sin14°+sin45°cos14°)=√2sin59°(辅助角公式)
b=sin16°+cos16°=√2sin(16°+45°)=√2sin61°
c=√6/6=√2*√3/6
则b>a>√2sin45°=1>c
即b>a>c
(可是,怎么觉得判断c那点不大漂亮,总觉得是题印错了,应该是c=√6/2)
则c=√2*√3/2=√2sin60°
得b>c>a
a=sin14°+cos14°=√2(cos45°sin14°+sin45°cos14°)=√2sin59°(辅助角公式)
b=sin16°+cos16°=√2sin(16°+45°)=√2sin61°
c=√6/6=√2*√3/6
则b>a>√2sin45°=1>c
即b>a>c
(可是,怎么觉得判断c那点不大漂亮,总觉得是题印错了,应该是c=√6/2)
则c=√2*√3/2=√2sin60°
得b>c>a