tana=1/cota
所以tana*cota=k^2-3=1
k=±2
tana+cota=k=±2
3π＜α＜（7π）/2,即在第三象限
tana>0
所以k=2
tana+1/tana=2
(tana)^2-2tana+1=0
所以tana=1
a=13π/4
cos(3π+a)+sin(π+a)
=cos(25π/4)+sin(17π/4)
=cos(π/4)+sin(π/4)
=√2