函数y=cos^6(x)+sin^6(x)的周期是多少

y=[cos^2(x)]^3+[sin^2(x)]^3
=[cos^2(x)+sin^2(x)][cos^4(x)+sin^4(x)-cos^2(x)*sin^2(x)]
立方和
=cos^4(x)+sin^4(x)-cos^2(x)*sin^2(x)
==[cos^2(x)+sin^2(x)]^2-2cos^2(x)*sin^2(x))-cos^2(x)*sin^2(x)
=1-3cos^2(x)*sin^2(x)
=1-(3/4)*(2cosxsinx)^2
=1-(3/4)*(sin2x)^2
=5/8+[3/8-(3/4)*(sin2x)^2]
=5/8+(3/8)[1-2*(sin2x)^2]
=(3/8)cos4x+5/8
T=2π/4=π/2

是pi/2
cos^6(x+pi/2)+sin^6(x+pi/2)
=(-sin(x))^6+(cos(x))^6
=sin^6(x)+cos^6(x)
如果不相信可以用几何画板试一试

qqq