Question

一道高中三角函数数学题，急求解，在线等！

10度的余弦乘30度的余弦乘50度的余弦乘70度的余弦等于？

Answer 1

cos10 cos30 cos50 cos70
= cos10 cos70 cos50 cos30
= 1/2(cos80 + cos60) cos50 cos30
= 1/2(cos80 cos50 + cos60 cos50) cos30
= 1/2[(cos130 + cos30)/2 + cos50 /2)] cos30
= 1/4[- cos50 + cos30 + cos50] cos30
= 1/4cos30 cos30
= 3/16

Answer 2

积化和差公式就行
cos10 cos30 cos50 cos70
= cos10 cos70 cos50 cos30
= 1/2(cos80 + cos60) cos50 cos30
= 1/2(cos80 cos50 + cos60 cos50) cos30
= 1/2[(cos130 + cos30)/2 + cos50 /2)] cos30
= 1/4[- cos50 + cos30 + cos50] cos30
= 1/4cos30 cos30
= 3/16