sin²1°+sin²2°+sin²3°+...+sin²90°的值
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/03 14:11:31
![sin²1°+sin²2°+sin²3°+...+sin²90°的值](/uploads/image/z/3727723-67-3.jpg?t=sin%26%23178%3B1%C2%B0%2Bsin%26%23178%3B2%C2%B0%2Bsin%26%23178%3B3%C2%B0%2B...%2Bsin%26%23178%3B90%C2%B0%E7%9A%84%E5%80%BC)
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sin²1°+sin²2°+sin²3°+...+sin²90°的值
sin²1°+sin²2°+sin²3°+...+sin²90°的值
sin²1°+sin²2°+sin²3°+...+sin²90°的值
sin²1°+sin²2°+sin²3°+…+sin²88°+sin²89°+sin²90°
=sin²1°+sin²2°+sin²3°+…sin²44°+sin²45°+sin²46°+…+sin²88°+sin²89°+sin²90°
=sin²1°+sin²2°+…+sin²44°+sin²45°+sin²46°+…+sin²88°+sin²89°+sin²90°
=sin²1°+sin²2°+…+sin²44°+sin²45°+cos²44°+…+cos²2°+cos²1°+sin²90°
=(sin²1°+cso²1°)+(sin²2°+cos²2°)+…+(sin²44°+cos²44°)+sin²45°+sin²90°
=1+1+……+1+(1/2)+1
=44+(1/2)+1
=45+(1/2)
=91/2