Question

已知sinα＝1/2+cosα,且αε（0,兀/2）,则cos2α/sin（α-兀/4）的值为

Answer 1

(sina－cosa)²=1－2sinacosa=1/4,则：2sinacosa=3/4,则1＋2sinacosa=7/4,即：(cosa＋sina)²=7/4,因sina、cosa都是正,则cosa＋sina=√7/2.而cos(2a)/sin(a－π/4)=sin(π/2－2a)/sin(a－π/4)=－{sin[2(a－π/4)]/[sin(a－π/4)]=－2cos(a－π/4)=－(√2cosa＋√2sina)=－(√2)×(√7/2)=－√14/2