cos方73+ cos方47 +cos73cos47
答案:1 悬赏:30 手机版
解决时间 2021-12-01 22:57
- 提问者网友：沉默的哀伤
- 2021-12-01 09:27
cos方73+ cos方47 +cos73cos47
最佳答案
- 五星知识达人网友：拜訪者
- 2021-12-01 10:11
解:
cos^2(73)+cos^2(47)+cos(73)cos(47)
=[cos(120-47)]^2+cos^2(47)+cos(120-47)cos(47)
={-0.5cos(47)+[(/3)/2]sin(47)}^2+cos^2(47)+{-0.5cos(47)+[(/3)/2]sin(47)}cos(47)
=cos^2(47)/4+3sin^2(47)/4-/3cos(47)sin(47)/2+cos^2(47)-cos^2(47)/2+/3sin(47)cos(47)
=(3/4)[sin^2(47)+cos^2(47)]
=3/4
cos^2(73)+cos^2(47)+cos(73)cos(47)
=[cos(120-47)]^2+cos^2(47)+cos(120-47)cos(47)
={-0.5cos(47)+[(/3)/2]sin(47)}^2+cos^2(47)+{-0.5cos(47)+[(/3)/2]sin(47)}cos(47)
=cos^2(47)/4+3sin^2(47)/4-/3cos(47)sin(47)/2+cos^2(47)-cos^2(47)/2+/3sin(47)cos(47)
=(3/4)[sin^2(47)+cos^2(47)]
=3/4
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