Question

已知函数f（x）=4cosxsin（x+π/6）-1

Answer 1

f(x)=4cosx(sinxcosπ/6+cosxsinπ/6)+1

=2√3sinxcosx+2cos²x-1+2

=√3sin2x+cos2x+2

=2(sin2x*√3/2+cos2x*1/2)+2

=2(sin2xcosπ/6+cos2xsinπ/6)+2

=2sin(2x+π/6)+2

所以T=2π/2=π

-π/6