f(x)=cos(x ＋圆周率/2)cos(x ＋圆周率/6)的最小正周期是多少?

f(x)=cos(x ＋圆周率/2)cos(x ＋圆周率/6)的最小正周期是多少?
f(x)=cos(x ＋圆周率/2)cos(x ＋圆周率/6)的最小正周期是多少?

f(x)=cos(x ＋圆周率/2)cos(x ＋圆周率/6)的最小正周期是多少?
f(x) =cos(x+π/2)cos(x+π/6)
= (cos( 2x+2π/3)+ cos(π/3))/2
= cos( 2x+2π/3) /2 + 1/4
最小正周期 = π

f(x)=cos(x ＋圆周率/2)cos(x ＋圆周率/6)
=-sinx*(cosx*根号3/2-sinx*1/2)
=1/2(sinx)^2-根号3/2 sinxcosx
=1/2*(1-cos2x)/2-根号3/2*1/2sin2x
=1/4-1/2(1/2cos2x-根号3/2sin2x)
=1/4-1/2cos(2x+Pai/3)
故最小正周期T=2Pai/2=Pai.