cos(x)*cos(x/2)*cos(x/4)*cos(x/8)......cos(x/(2^(n-1))

cos(x)*cos(x/2)*cos(x/4)*cos(x/8)......cos(x/(2^(n-1))
=cos(x)*cos(x/2)*cos(x/4)*cos(x/8)......cos(x/(2^(n-1))sin(x/(2^(n-1)) /sin(x/2^(n-1))
=cos(x)*cos(x/2)*cos(x/4)*cos(x/8)......sin(x/(2^(n-2)) /2sin(x/2^(n-1))
=...
=cos(x)*cos(x/2)*cos(x/4)*cos(x/8)sin(x/8) /2^(n-4)*sin(x/2^(n-1))
=cos(x)*cos(x/2)*cos(x/4)sin(x/4) /2^(n-3)*sin(x/2^(n-1))
=cos(x)*cos(x/2)*sin(x/2) /2^(n-2)*sin(x/2^(n-1))
=cos(x)*sin(x) /2^(n-1)sin(x/2^(n-1))
=sin(2x) / [2^nsin(x/2^(n-1))]

在等式的最后乘以sin(x/(2^(n-1))),然后从后面向前面逐步应用正弦的二倍角公式，即可得到简化后的答案。