作业帮【三脚函数!】sin6°sin42°sin66°sin78°还有一题：sin²20°+cos²50°+sin20°+cos50°求值
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/04 07:58:09
【三脚函数!】sin6°sin42°sin66°sin78°还有一题：sin²20°+cos²50°+sin20°+cos50°求值
【三脚函数!】sin6°sin42°sin66°sin78°
还有一题：
sin²20°+cos²50°+sin20°+cos50°
求值
【三脚函数!】sin6°sin42°sin66°sin78°还有一题：sin²20°+cos²50°+sin20°+cos50°求值
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°/16cos6°
=sin6°/16cos6°
=1/16
sin6°sin42°sin66°sin78°
=sin6°cos48°cos24°cos12°
=sin6°cos12°cos24°cos48°
=2cos6°sin6°cos12°cos24°cos48°/2cos6°
=sin12°cos12°cos24°cos48°/2cos6°
=sin24°cos24°cos48°/4cos6°
=sin...
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sin6°sin42°sin66°sin78°
=sin6°cos48°cos24°cos12°
=sin6°cos12°cos24°cos48°
=2cos6°sin6°cos12°cos24°cos48°/2cos6°
=sin12°cos12°cos24°cos48°/2cos6°
=sin24°cos24°cos48°/4cos6°
=sin48°cos48°/8cos6°
=sin96°/16cos6°
=1/16
<因为根据诱导公式，sin96°=cos6°>
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