证明:函数f(x)=cos^2+cos^2(x+π/3)+cos^2(x-π/3)是常数函数
问题描述:
证明:函数f(x)=cos^2+cos^2(x+π/3)+cos^2(x-π/3)是常数函数
答
cos^2(x+π/3)+cos^2(x-π/3)=(cosx/2-根号3*sinx/2)^2+(cosx/2+根号3*sinx/2)^2=(cosx)^2/2+3(sinx)^2/2=1/2+(sinx)^2f(x)=cos^2x+cos^2(x+π/3)+cos^2(x-π/3)=(cosx)^2+1/2+(sinx)^2=3/2,