函数y=sin(4次方)x+cos(4次方)x的最小正周期是?
问题描述：
函数y=sin(4次方)x+cos(4次方)x的最小正周期是?
答
y=(sinx)^4+(cosx)^4=[(sinx)^2+(cosx)^2]^2-2(sinx)^2(cosx)^2=1-(1/2)[sin(2x)]^2=1-(1/4)2[sin(2x)]^2=1/4-(1/4)2[sin(2x)]^2+3/4=(1/4){1-2[sin(2x)]^2}+3/4=(1/4)cos(4x)+3/4则最小正周期T=2π/4=π/2.