Question

关于三角函数的一道题（高中）

cos(10)*cos(20)*cos(40)=?
类似cos(X)*cos(2x)*cos(4x)=? sin(x)*sin(2x)*sin(4x)=?的题目有没有什么规律

要有过程

Answer 1

cos(10)*cos(20)*cos(40)
=sin(10)*cos(10)*cos(20)*cos(40)
=1/2sin(20)*cos(20)*cos(40)
=1/2*1/2*sin(40)*cos(40)
=1/2*1/2*1/2*sin(80)
=1/8*cos(10)
规律不用我说了吧:)
这种东西叫等比余弦积

Answer 2

cos(10)*cos(20)*cos(40)
=2sin(10)cos(10)*cos(20)*cos(40)/[2sin(10)]
=sin(20)*cos(20)*cos(40)/[2sin(10)]
=2sin(20)*cos(20)*cos(40)/[4sin(10)]
=sin(40)*cos(40)/[4sin(10)]
=2sin(40)*cos(40)/[8sin(10)]
=sin(80)/[8sin(10)]
=sin(80)/[8cos(10)]
=tan(80)/8

就是乘以sin(x)或cos(x)凑成sin(2x)

Answer 3

sin(8x)/(8sinx)