已知向量a=(cosx,y),b=(根号三sinx+cosx,-1)(x,y∈R),且ab=0

(1)a*b=cosx(√3sinx+cosx)-y
=√3sinxcosx+cos²x-y
=√3/2*sin2x+1/2*(1+cos2x)-y
=√3/2*sin2x+1/2*cos2x+1/2-y
=sin(2x+π/6)+1/2-y
=0
∴f(x)=y=sin(2x+π/6)+1/2
(2)f(x)=sin(2x+π/6)+1/2=1
∴sin(2x+π/6)=1/2,而0≤x≤π/2
∴π/6≤2x+π/6≤7π/6
∴2x+π/6=π/6,或5π/6
∴x=0,或π/3
望采纳