已知a属于(π/2,π),且4sina=-3cosa,求cos(a+π/4)/sin2a的值

问题描述:

已知a属于(π/2,π),且4sina=-3cosa,求cos(a+π/4)/sin2a的值

tana=-3/4
a属于(π/2,π),sina>0,cosa(cosa)^2=1/[1+(tanx)^2]=16/25
cosa=-4/5
sina=tanacosa=3/5
sin2a=2sinacosa=-24/25
cos(a+π/4)=cosacos(π/4)-sinasin(π/4)=-7√2/10
cos(a+π/4)/sin2a=35√2/48