求值cos12 ° X cos24° X cos48° X cos84°求解!

cos12° * cos24° * cos48° * cos84°
=2sin12° *cos12° * cos24° * cos48° * cos84°/2 sin12°
=sin24°*cos24° * cos48° * cos84°/2 sin12°
=2sin24°*cos24° * cos48° * cos84°/4 sin12°
=sin48° * cos48° * cos84°/4 sin12°
=2sin48° * cos48° * cos84°/8 sin12°
=sin96° * cos84°/8sin12°
=sin84° * cos84°/8sin12°
=sin168°/16sin12°
=sin12°/16sin12°
=1/16

前面配一个sin12然后使用sin2x= 2sinxcosx求解

cos12°cos24°cos48°cos84°
观察知：(最大的度数先不用管）
48为24的2倍
24为12的2倍
且均为余弦
针对此类题 应乘以一个最小度数的正弦
如下：
=sin12°cos12°cos24°cos48°cos84°/sin12°
=2sin12°cos12°cos24°cos48°cos84°/2sin12°