f(x)=√3sinxcosx+cos²x+a=√3/2sin2x+1/2cos2x+1/2+a=sin(2x+π/6)+a+1/2∵x∈[-π/6,π/3]∴2x∈[-π/3,2π/3]∴2x+π/6∈[-π/6,5π/6]∴2x+π/6=-π/6时,f(x)min=-1/2+a+1/2=a2x+π/6=π/2时,f(x)max=1+a+1...