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- Feb 14, 2012
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Let $a,\,b,\,c$ and $d$ be real numbers that satisfy the equation $f(x)=a\cos x+b\cos 2x+c\cos 3x+d\cos 4x \le 1$ for any real number $x$. Find the values of $a,\,b,\,c$ and $d$ such that $a+b-c+d$ takes the maximum number.