已知向量a=(根号3,-1),b=(sin2x,cos2x),设函数f(x)=a*b,若f(x)=0,（1）求tanx的值,

(1)f(x)=√3sin2x-cos2x=2sin(2x-π/6)=0,即√3sin2x-cos2x=0,tan2x=√3/3.
tan2x=2tanx/[1-(tanx)^2]=√3/3,(tanx)^2+2√3tanx-1=0,tanx=-√3-4或tanx=-√3+4.
(2)2kπ-π/2