化简求值cos146°+cos94°+2cos47°cos73°
答案:1 悬赏:70 手机版
解决时间 2021-11-24 19:34
- 提问者网友：蓝莓格格巫
- 2021-11-24 08:49
化简求值cos146°+cos94°+2cos47°cos73°
最佳答案
- 五星知识达人网友：蕴藏春秋
- 2021-11-24 10:01
解答：
cos146°+cos94°+2cos47°cos73°
= cos(120°+26°)+cos(120°-26°)+(cos47°cos73°-sin47°sin73°)+(cos47°cos73°+sin47°sin73°)
=cos120°cos26°-sin120°sin26°+cos120°cos26°+sin120°sin26°+cos(47°+73°)+cos(47°-73°)
=2cos120°cos26°+cos120°+cos26°
=-cos26°+cos120°+cos26°
=cos120°
=-cos60°
=-1/2
cos146°+cos94°+2cos47°cos73°
= cos(120°+26°)+cos(120°-26°)+(cos47°cos73°-sin47°sin73°)+(cos47°cos73°+sin47°sin73°)
=cos120°cos26°-sin120°sin26°+cos120°cos26°+sin120°sin26°+cos(47°+73°)+cos(47°-73°)
=2cos120°cos26°+cos120°+cos26°
=-cos26°+cos120°+cos26°
=cos120°
=-cos60°
=-1/2
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