函数y=2sin(π/6-x)+2cosx（x∈R)的最小值

y=2sin(π/6-x)+2cosx=2[sin(π/6)×cosx-cos(π/6)×sinx]+2cosx=cosx-√3sinx+2cosx
=3cosx-√3sinx=2√3(√3/2cosx-1/2sinx)=2√3sin(π/3-x)
当π/3-x=-1时,最小值f(x)min=-2√3