tana+1/tana=sina/cosa+cosa/sina=[(sina)^2+(cosa)^2]/sinacosa=1/[1/2*2sinacos]
=2/sin2a=10/3
sin2a=3/5
π/4π/2<2a<π
所以cos2a<0
因为(sin2a)^2+(cos2a)^2=1
所以cos2a=-4/5
sin(2a+π/2)=cos2a=-4/5