向量a+b=(cos3x/2+cosx/2,sin3x/2-sinx/2)
=(2cosxcosx/2,2cosxsinx/2),
|a+b|=√[4（cosx)^2(cosx/2)^2+4(cosx)^2(sinx/2)^2]
=2√（cosx)^2[(cosx/2)^2+(sinx/2)^2]
=2√(cosx)^2*1
=2|cosx|,
∵x∈[π/2,3π/2],
∴cosx≤0,
∴|a+b|=-2cosx,
2、f(x)=2sinx+│a+b│=2sinx-2cosx
=2√2[sinx*(√2/2）-cosx*(√2/2)]
=2√2sin(x-π/4）,
∵x∈[π/2,3π/2],
∴(x-π/4）∈[π/4,5π/4],
当(x-π/4）=π时,函数有最小值为-1,
∴f(x)(min)=-2√2.