已知不等式f（x）=3根号2sinx/4cosx/4+根号6cos²x/4-根号6/2-m≤0对于任意的-5π

f（x）=3√2sinx/4cosx/4+√6cos²x/4-√6/2-m
=3√2/2sin(x/2)+√6/2(1+cosx/2)-√6/2-m
=3√2/2*sin(x/2)+√6/2*cosx/2)-m
=√6[√3/2*sinx/2+1/2*cosx/2]-m
=√6sin(x/2+π/6)-m
∵对于任意的-5π/6≤x≤π/6,f(x)≤0
∴f(x)max≤0
∵-5π/6≤x≤π/6
∴-5π/12≤x/2≤π/12
∴-π/4≤x/2+π/6≤π/4
∴当x/2+π/6=π/4时,
f(x)取得最大值√6*√2/2-m=√3-m
∴√3-m≤0
∴m≥√3