由根与系数的关系:tana+cota=k,tana×cota=k²-3,k²-3=1,k=±2tana+cota=±2,sin(2a)=2/(tana+cota)=±1,∴2a=2kπ+π/2∵3π<a<7π/2,∴a=3π+π/4,sina=sin(3π+π/4)=-sinπ/4=-√2/2,cosa=cos(3π+π/4)=-cosπ/4=-√2/2