cos12°-cos24°-cos48°+cos84°

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/02 17:40:31
cos12°-cos24°-cos48°+cos84°
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cos12°-cos24°-cos48°+cos84°
cos12°-cos24°-cos48°+cos84°

cos12°-cos24°-cos48°+cos84°
cos12°-cos24°-cos48°+cos84°
=cos12°+cos84°-cos24°-cos48°
=2cos48°cos36°-2cos36°cos12°
=2cos36°(cos48°-cos12°)
=-2cos36°2sin30°sin18°
=-2cos36°sin18°
=-2cos36°cos72°
=-2(√5+1)/4*[2(√5+1)^2/16-1]
=-1/2

用倍·角公式先把cos84°换沉cos48 在用倍·角公式换成os24 最后变成cos12°

cos12°-cos24°-cos48°+cos84°
=cos12°+cos84°-(cos24°+cos48°)
=2cos48°cos36°-2cos36°cos12°
=2cos36°(cos48°-cos12°)
=2cos36°(-2sin30°sin18°)
=-2cos36°(sin18°)