注意诱导公式sin(π/2-α）=cosα
y=2sin( π/3 -x)-cos( π/6 +x)
=2sin( π/3 -x)-sin[π/2-( π/6 +x)]
=2sin( π/3 -x)-sin( π/3 -x)
=sin( π/3 -x)
即得y=sin( π/3 -x)
所以最小值为-1.