sin（α+ π/4）=sinαcosπ/4+cosαsinπ/4=√2/2(sinα+cosα)=√2/5所以sinα+cosα=2/5所以(sinα+cosα)²=4/25又(sinα+cosα)²=sin²α+2sinαcosα+cos²α=1+2sinαcosα=1+sin2α=4/25所...