数学问题~~HELP ME~!

问题描述:

数学问题~~HELP ME~!
f(x)=cosx-1/2cos2x(x∈R)的最大值等于_______
谢谢啦~最好点拨我一下啦~~!

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-1f(t)=-t^2+t+1/2
f(t)最大值为f(1/2)=3/4