函数y=sin(x-π/3）+cos（x+7π/6）的最小值是多少

题目

函数y=sin(x-π/3）+cos（x+7π/6）的最小值是多少

答案

y=sin(x-π/3）+cos(π+x+π/6）
=sin(x-π/3)-cos(x+π/6)
=sin(x-π/3)-sin[π/2-(x+π/6)]
=sin(x-π/3)-sin(π/3-x)
=sin(x-π/3)+sin(x-π/3)
=2sin(x-π/3)
所以最小值=-2