已知6(sina)^2+sinacosa-2(cosa)^2=0 a属于[TT/2,TT) 求sin(2a+TT/3)已知6(sina)^2+sinacosa-2(cosa)^2 a属于[TT/2,TT) 求sin(2a+TT/3)
问题描述:
已知6(sina)^2+sinacosa-2(cosa)^2=0 a属于[TT/2,TT) 求sin(2a+TT/3)
已知6(sina)^2+sinacosa-2(cosa)^2 a属于[TT/2,TT) 求sin(2a+TT/3)
答
因式分解(3sina+2cosa)(2sina-cosa)=0sina/cosa=-2/3或1/2(舍)(sina)^2/(cosa)^2=4/9(sina)^2/[1-(sina)^2]=4/9(sina)^2=4/5sina=2/√5,cosa=-1/√5sin2a=2*2/√5*(-1/√5)=-4/5cos2a=1/5sin(2a+TT/3)=(√3-4)/10...