IMO 1977 SL 7

Let a, b, A, B be given constant real numbers and

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IMO 1977 SL 7

Origin: GBR

Problem

Let a, b, A, B be given constant real numbers and f(x) = 1 −a cos x −b sin x −A cos 2x −B sin 2x. Prove that if f(x) \geq0 for all real x, then a2 + b2 \leq2 and A2 + B2 \leq1.