sin²10°+sin²20°+sin²30°+……+sin²80°+sin²90°=?
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/09 05:55:17
![sin²10°+sin²20°+sin²30°+……+sin²80°+sin²90°=?](/uploads/image/z/972452-20-2.jpg?t=sin%26%23178%3B10%C2%B0%2Bsin%26%23178%3B20%C2%B0%2Bsin%26%23178%3B30%C2%B0%2B%E2%80%A6%E2%80%A6%2Bsin%26%23178%3B80%C2%B0%2Bsin%26%23178%3B90%C2%B0%3D%3F)
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sin²10°+sin²20°+sin²30°+……+sin²80°+sin²90°=?
sin²10°+sin²20°+sin²30°+……+sin²80°+sin²90°=?
sin²10°+sin²20°+sin²30°+……+sin²80°+sin²90°=?
sin80=sin(90-10)=cos10
sin²10+sin²80=sin²10+cos²10=1
同理
sin²20+sin²70=1
sin²30+sin²60=1
sin²40+sin²50=1
sin²90°=1
所以原式=5
5