设函数f(x)=(cosx)^2+根号3*sinxcosx+a若x∈【0,π/2】时,f(x)的最小值为2,求a的值

f(x)=(cos2x+1)/2+√3*sin2x/2+a
=sin(2x+π/6)+1/2+a
所以当x∈[0,π/2]
那么
2x+π/6∈[π/6,7π/6]
所以最小值
f(x)=sin(7π/6)+1/2+a
=-1/2+1/2+a
=a=2
所以a=2