高中数学题，寻求解答办法。要详细过程 谢谢。

∵tana+cota=5/2
==>sina/cosa+cosa/sina=5/2
==>(sin²a+cos²a)/(sinacosa)=5/2
==>1/(sinacosa)=5/2
==>sinacosa=2/5
==>sin(2a)=4/5
又π/4<a<π/2,则π/2<2a<π
∴cos(2a)<0
故 cos(2a)=-√(1-sin²(2a))=-3/5
sin(2a+π/4)=sin(2a)cos(π/4)+cos(2a)sin(π/4)
=(4/5)(√2/2)+(-3/5)(√2/2)
=√2/10.