a属于(0,π/2),且2sin2a-sinacosa-3cos2a=o.求{sin(a+π/4)}/(sin2a+coa2a+1)
问题描述:
a属于(0,π/2),且2sin2a-sinacosa-3cos2a=o.求{sin(a+π/4)}/(sin2a+coa2a+1)
答
2sin^2a-sinacosa-3cos^2a=0(2sina-3cosa)(sina+cosa)=0∵0<a<π/2∴sina>0,cosa>0∴sina+cosa>0≠0∴2sina-3cosa=0∵sin^2a+cos^2a=1解得:sina=3√13/13cosa=2√13/13∴sin(a+π/4)/sin2a+cos2a+1=[√2/2(...