已知函数f(x)=sin(2x+π/3)+sin(2x-π/3)+2cos^2x-1

问题描述:

已知函数f(x)=sin(2x+π/3)+sin(2x-π/3)+2cos^2x-1
求f(x)在区间{-π/4,π/4}上的最大值和最小值
x∈[-π/4,π/4]①
2x∈[-π/2,π/2]②
2x+π/4∈[-π/4,3π/4]③
-1

2x+π/4∈[-π/4,3π/4]可以去到正弦值最大的角π/2,可以去到正弦值最小的角-π/4
所以-√2/2=