f(X)=√3/2sin2x-1/2cos2x-1=sin(2x-π/6）-1
g(x)=f(x+π/6)=sin(2x+π/6)-1
①f(C)=sin(2C-π/6）-1=0
2C-π/6=π/2
C=π/3
sinB=3sinA=sin(A+C) 5/2sinA=√3/2cosA sinA=√21/14 sinB=3√21/14
有正弦定理得
a=3/4 b=9/4
②g(B)=0 B=π/6
m*n=cosA+√3/2(sinA-√3/3cosA)=√3/2sinA+1/2sinA=sin(A+π/6)∈ (0,1)