若cos2a/sin(a-45°)=-根号2/2,则cosa+sina的值为?
问题描述：
若cos2a/sin(a-45°)=-根号2/2,则cosa+sina的值为?
答
cos2a=(cosa)^2-(sina)^2
sin(a-45°)=√2/2(sina-cosa)
∴cos2a/sin(a-45°)=-√2(sina+cosa)=-√2/2
∴cosa+sina=1/2