Question 67
Let real numbers $a, b, c$ and $d$ satisfy
$$
f(x) = a \cos x + b \cos 2x + c \cos 3x + d \cos 4x \le 1
$$
for any real number $x$. Find the values of $a, b, c$ and $d$ such that $a + b - c + d$ takes the maximum number. (posed by Li Shenghong)
$$
f(x) = a \cos x + b \cos 2x + c \cos 3x + d \cos 4x \le 1
$$
for any real number $x$. Find the values of $a, b, c$ and $d$ such that $a + b - c + d$ takes the maximum number. (posed by Li Shenghong)