f(x)=2sin(sinx+cosx)

题目

f(x)=2sin(sinx+cosx)
1.求f（x）最小正周期和最大值
2.求f（x）的增区间

答案

f(x)=2sinx(sinx+cosx)
=2sin^2x+2sinxcosx
=2sinxcosx+2sin^2x-1+1
=sin2x-cos2x+1
=根号2sin(2x-π/4)+1
(1)
f（x）最小正周期π 最大值=根号2+1
(2) 增区间 2kπ-π/2