Question 7
(GBR 2) IMO4. Let $a,b,A,B$ be given constant real numbers and
$$f(x)=1-a\cos x-b\sin x-A\cos2x-B\sin2x.$$
Prove that if $f(x)\ge0$ for all real $x$, then
$$a^2+b^2\le2\qquad A^2+B^2\le1.$$
$$f(x)=1-a\cos x-b\sin x-A\cos2x-B\sin2x.$$
Prove that if $f(x)\ge0$ for all real $x$, then
$$a^2+b^2\le2\qquad A^2+B^2\le1.$$