Question

求函数f(x)=cos^2x+2√3sinxcosx-sin^2x的周期和单调区间

求函数f(x)=cos^2x+2√3sinxcosx-sin^2x的周期和单调区间
谢谢！

Answer 1

f(x)=cos^2x+2√3sinxcosx-sin^2x
=cos^2x-sin^2x+2√3sinxcosx
=cos2x+2√3sinxcosx
=cos2x+√3sin2x
=2[(1/2)*cos2x+(√3/2)*sin2x]
=2*sin（2x+π/6）
=2*sin[2(x+π/12)]
周期为2π/2=π

单调区间为：
[kπ-π/3,kπ+π/6)上单调增；
[kπ+π/6,kπ+2π/3)上单调减。