sin6°sin42°sin66°sin78°求值
问题描述：
sin6°sin42°sin66°sin78°求值
答
sin6°sin42°sin66°sin78°
=sin6°cos12°cos24°cos48°
=16cos6°sin6°cos12°cos24°cos48°/16cos6°
=8sin12°cos12°cos24°cos48°/16cos6°
=4sin24°cos24°cos48°/16cos6°
=2sin48°cos48°/16cos6°
=sin96°/16cos6°
=cos6°/16cos6°
=1/16
答
原式=sin6°cos12°cos24°cos48°
=8cos6°sin6°cos12°cos24°cos48°/8cos6°
=4sin12°cos12°cos24°cos48°/8cos6°
=2sin24°cos24°cos48°/8cos6°
=sin48°cos48°/8cos6°
=sin96°/16cos6°
=sin6°/16cos6°
=1/16
答：原式的值为1/16
答
sin6°sin42°sin66°sin78°=sin6°cos12°cos24°cos48°=8cos6°sin6°cos12°cos24°cos48°/8cos6°=4sin12°cos12°cos24°cos48°/8cos6°=2sin24°cos24°cos48°/8cos6°=sin48°cos48°/8cos6°=sin96°/1...