已知函数f（x）=2cos（x- 2∏/3）+2cosx,x属于2/∏,∏ 求函数的值域

f(x)=2cosxcos(2π/3)+2sinxsin(2π/3)+2cosx
=（-1/2）x2cosx+（√3/2）x2sinx+2cosx
=√3sinx+cosx
=2sin(x+π/6)
∵ x∈[π/2,π]
则 x+π/6∈[2π/3,7π/6]
∴ sin(x+π/6)∈[-1/2,√3/2]
即2sin(x+π/6)∈[-1,√3]