sin²1°+sin²2°+sin²3°+...+sin²90°的值

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/11/08 00:50:44

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

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