若tana+1/tana=10/3,a属于（π/4,π/2）,则sin(2a+π/2)的值为

题目

若tana+1/tana=10/3,a属于（π/4,π/2）,则sin(2a+π/2)的值为
A-根号2/10 B根号2/10 C5根号2/10 D7根号2/10
你答案算错了应该选D

答案

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