∵sinα=1/2+cosα∴sinα-cosα=1/2则 (sinα-cosα)²=1/4∴ 1-2sinα*cosα=1/4∴ sin2α=3/4∴1+sin2α=1+3/4∴(sinα+cosα)²=7/4又 α∈(0,π/2)∴ sinα>0,cosα>0∴ sinα+cosα=√7/2原式=cos2α/...