cos2α/sin(α-π/4)=√2/2 求sinα+cosα的值

发布时间:2021-03-16 09:02:59

cos2α/sin(α-π/4)=√2/2 求sinα+cosα的值

网友回答

cos2a=cos²a-sin²a=(cosa+sina)(cosa-sina)
sin(a-π/4)=sinasinπ/4-cosacosπ/4=√2/2 (sina-cosa)
cos2a/sin(a-π/4)=√2/2
(cosa+sina)(cosa-sina)/[√2/2 (sina-cosa)]=√2/2
cosa+sina=-1/2
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