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展开全部
sin²1°+sin²2°+...+sin²89°
=sin²1°+sin²2°+...sin²44°+sin²45°+sin²(90°-44°)+……+sin²(90°-1°)
=sin²1°+sin²2°+...sin²44°+sin²45°+cos²44°+……+cos²1°
=(sin²1°+cos²1°)+(sin²2°+cos²2°)+...+(sin²44°+cos²44°)+sin²45°
=44+1/2
=sin²1°+sin²2°+...sin²44°+sin²45°+sin²(90°-44°)+……+sin²(90°-1°)
=sin²1°+sin²2°+...sin²44°+sin²45°+cos²44°+……+cos²1°
=(sin²1°+cos²1°)+(sin²2°+cos²2°)+...+(sin²44°+cos²44°)+sin²45°
=44+1/2
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展开全部
(sin89)^2=[sin(90-1)]^2=(sin90cos1-cos90sin1)^2=(cos1)^2
(sin1)^2+(cos1)^2=1
原式=44+(sin45)^2=99/2
(sin1)^2+(cos1)^2=1
原式=44+(sin45)^2=99/2
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