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

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

cos2a/sin(a-π/4)=(cos^a-sin^a)/[√2/2(sina-cosa)]=-√2(sina+cosa)
设(sina+cosa)=t,题设sina-cosa=1/2,则sina=(t+1/2)/2,cosa=(t-1/2)/2,
因为(sina)^2+(cosa)^2=1,求出t=√7/2
y=-√14/2

∵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...