f(x)=cos2x*1/2-sin2x*√3/2+√3*sin2x+2a
=1/2*cos2x+√3/2*sin2x+2a
=sinπ/6*cos2x+cosπ/6*sin2x+2a
=sin(2x+π/6)+2a
因为0≤x≤π/4,那么π/6≤2x+π/6≤2π/3
那么1/2≤sin(2x+π/6)≤1
所以f(x)min=1/2+2a=0
那么a=-1/4
f(x)=cos2x*1/2-sin2x*√3/2+√3*sin2x+2a
=1/2*cos2x+√3/2*sin2x+2a
=sinπ/6*cos2x+cosπ/6*sin2x+2a
=sin(2x+π/6)+2a
因为0≤x≤π/4,那么π/6≤2x+π/6≤2π/3
那么1/2≤sin(2x+π/6)≤1
所以f(x)min=1/2+2a=0
那么a=-1/4