若cos2α/sin（α-π/4）=二分之根号二,那么sinα+cosα=?

网友回答

即(cos²α-sin²α)/(sinαcosπ/4-cosαsinπ/4)=√2/2
(cosα-sinα)(cosα+sinα)/[-√2/2(cosα-sinα)]=√2/2
所以cosα+sinα=-1/2