Question

已知f(x)=cos^(x+θ)-2cosθcosxcos(x+θ)+cos^θ求f(x)的最大值、最小值和最小正周期!

Answer 1

f(x)=cos(x+θ)[cos(x+θ)-2cosθcosx]+cos^2θ

=-cos(x+θ)[sinxsinθ+cosxcosθ]+cos^2θ

=-cos(x+θ)cos(x-θ)+cos^2θ

=-(cosx)/2-(cosθ)/2+cos^2θ

f(x)的最大值1+cos^2θ-(cosθ)/2、最小值-1+cos^2θ-(cosθ)/2,最小正周期2π