1/2cos2x=(cosx)^2-1/2
f(x)=cosx-1/2cos2x
=cosx-(cosx)^2+1/2
=-(cosx)^2+cosx+1/2(x∈R)
令t=cosx,则-1<=t<=1
f(t)=-t^2+t+1/2
f(t)最大值为f(1/2)=3/4