函数f(x)=tanx(cos(x/2)^4-sin(x/2)^4)的最小正周期

题目

函数f(x)=tanx(cos(x/2)^4-sin(x/2)^4)的最小正周期

答案

f(x)=tanx[cos^4(x/2)-sin^4(x/2)]
=tanx{[cos^2(x/2)+sim^2(x/2)][cos^2(x/2)-sin^2(x/2)]}'
=tanx*cosx
=sinx
F(x)的最小正周期为2π.