已知sina=1/2+cosa,且a∈（0,π/2）,则cos2a/sin（a-π/4）的值为多少?

∵sina=1/2+cosa∴sina-cosa=1/2∴(sina-cosa)²=1/4∴1-2sinacosa=1/4∴2sinacosa=3/4∴(cosa+sina)²=1+2sinacosa=7/4∵a∈（0,π/2）∴cosa+sina>0∴cosa+sina=√7/2∴cos2a/sin（a-π/4）=(cos²a-s...