求值 cos10°cos20°cos40°

分类: 作业答案 • 2022-01-02 13:23:49

问题描述：

答

cos10*cos20*cos40 =2sin10cos10cos20cos40/(2sin10)=2sin20cos20cos40/(4sin10)
=2sin40cos40/(8sin10)=sin80/(8sin10)=cos10/(8sin10)=1/8*cot10

答

cos10°cos20°cos40°=2sin10° cos10°cos20°cos40°/2sin10°
=2sin20°cos20°cos40°/4sin10° =2sin40°cos40°/8sin10° =sin80°/8sin10° =tan80°/8