y=2sin(180/3-x)-cos(180/6+x0(x属于R）的最小值等于

题目

y=2sin(180/3-x)-cos(180/6+x0(x属于R）的最小值等于

答案

y=2sin(π/3-x)-cos(π/6+x)
=2√3/2cosx-2*1/2sinx-cosπ/6cosx+sinπ/6sinx
=√3cosx-sinx-√3/2cosx+1/2sinx
=√3/2cosx-1/2sinx
=cos(x+π/6)
y最小值= -1