已知sina=1/2+cosa,且a∈(0,π/2),则cos2a/sin(a-π/4)的值为多少?
问题描述:
已知sina=1/2+cosa,且a∈(0,π/2),则cos2a/sin(a-π/4)的值为多少?
不要复制粘贴的
答
∵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...