sin25°+sin210°+sin215°+...+sin280°+sin285°=?
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sin25°+sin210°+sin215°+...+sin280°+sin285°=?
sin25°+sin210°+sin215°+...+sin280°+sin285°=?
sin25°+sin210°+sin215°+...+sin280°+sin285°=?
1、观察285+210=280+215=275+220=270+225=...=245+250=495
2、计算sin285=sin(495-210)=√2/2(cos210+sin210)
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3、原式=sin25+sin210+...+sin240+sin245+√2/2(cos210+sin210+cos215+sin215...+cos245+sin245)
4、观察210+245=215+240=220+235=225+230=455
5、计算sin245=sin(455-210)=sin95x(cos210-sin210) cos245=cos95x(cos210+sin210)
6、原式==sin25+sin210+...+sin240+sin245+√2sin95(cos210+cos215+cos220+cos225)
最终可以消去sin25 得到一个常数
8.5
sin25°+sin210°+sin215°+...+sin280°+sin285°=?
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