（1）.∵sinx=4/5且x∈[π/2,π]∴cosx=-3/5∴f(x)=2sin(x+兀/6)-2cosx=√3sinx-cosx=√3×4/5-(-3/5)=4√3/5+3/5（2）∵f(x)=√3sinx-cosx=2sin(x-π/6),(x∈[π/2,π])∴-1≤f(x)≤2∴函数f(x)的值域是[-1,2(3)∵x...