Question

y=sin(x+pi/6)sin(x-pi/6)的最小正周期

Answer 1

y=(sinxcospi/6+cosxsinpi/6)(sinxcospi/6-cosxsinpi/6)

=(sinxcospi/6)^2-(cosxsinpi/6)^2

=3/4*(sinx)^2-1/4*(cosx)^2

=3/4*(1-cos2x)/2-1/4*(1+cos2x)/2

=3/4-3/8cos2x-1/4-1/8*cos2x

=-1/2*cos2x+1/2

所以T=2pi/2=pi