设f(x)=sinxcosx-√3cos(兀+x)cosx(x∈R)(1)求F(x)的最小正周期(2)求F(x)单调增
问题描述:
设f(x)=sinxcosx-√3cos(兀+x)cosx(x∈R)(1)求F(x)的最小正周期(2)求F(x)单调增
答
f(x)=sinxcosx-√3cos(兀+x)cosx
=1/2sin2x+√3cos^2x
=1/2sin2x+√3(cos2x-1)/2
=sin(2x+兀/3)-√3/2
最小正周期T=兀
2K兀-兀/2