△abc三内角a.b.c的对边分别为a.b.c,关于x的不等式x2cosc+4xsinc+6

x2cosc+4xsinc+6<0的解集为空集,判别式小于或等于0,
16(sinC)^2-24cosC≤0,
2(sinC)^2-3cosC≤0,
2-2(cosC)^2-3cosC≤0,
2(cosC)^2+3cosC-2≥0,
(2cosC-1)(cosC+2)≥0,
cosC≥1/2,
C的最大值为60度.