已知函数f(x)=5sinxcosx-5根3cos^2x+5根3/2,（X∈R),求f(x)的单调区间
问题描述：
已知函数f(x)=5sinxcosx-5根3cos^2x+5根3/2,（X∈R),求f(x)的单调区间
答
f(x)=5/2*sin2x-5√3*(1+cos2x)/2+5√3/2
=5/2*sin2x-5√3/2*cos2x
=5(sin2x*1/2-cos2x*√3/2)
=5(sin2xcosπ/3-cos2xsinπ/3)
=5sin(2x-π/3)
sinx增则2kπ-π/2
2kπ-π/22kπ-2π/3kπ-π/3
同理,减区间(kπ+π/6,kπ+2π/3)