20度、40度、80度三个角的余弦值的乘积的式子怎么化简?
问题描述：
20度、40度、80度三个角的余弦值的乘积的式子怎么化简?
答
cos20cos40cos80
=sin20cos20cos40cos80/sin20
=sin40cos40cos80/(2sin20)
=sin80cos80/(4sin20)
=sin160/(8sin20)
=sin(180-160)/(8sin20)
=sin20/8/sin20
=1/8