f(x)=2sin(x+π/6)-2cosx=2sinxcosπ/6+2cosxsinπ/6-2cosx
=√3sinx+cosx-2cosx
=√3sinx-cosx,
若sinx=4/5,x∈[π/2,π].则cosx=-3/5.
所以上式=(4√3+3)/5.
f(x)= √3sinx-cosx=2sin(x-π/6)
x∈[π/2,π],x-π/6∈[π/3,5π/6]
f(x) ∈[1,2].