cos2α/sin(α-π/4)=√2/2 求sinα+cosα的值
问题描述：
cos2α/sin(α-π/4)=√2/2 求sinα+cosα的值
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