y=cos(x)+sin(x+π/3),求最小正周期,最大值,单调区间……
问题描述：
y=cos(x)+sin(x+π/3),求最小正周期,最大值,单调区间……
答
y=cosx+sin(x+π/3)
=sin(π/2-x)+sin(x+π/3)
=2sin[(π/2-x+x+π/3)/2]cos(x+π/3-π/2+x)/2]
=2sin5π/12cos(x-π/12)
最小正周期=2π
最大值=2sin5π/12
单调递增:2kπ-π