Four real constants are given and f( ) = 1 - a - b - A 2 - B 2

MATHEMATICS · Subjective · A Level · Mathematics · Trigonometry · Trigonometry

Problem

Four real constants a,b,A,Ba, b, A, B are given and f(θ)=1−acos⁡θ−bsin⁡θ−Acos⁡2θ−Bsin⁡2θ.f(\theta) = 1 - a \cos \theta - b \sin \theta - A \cos 2\theta - B \sin 2\theta. Prove that if f(θ)≥0,∀θ∈Rf(\theta) \ge 0, \forall \theta \in R, then a2+b2≤2a^2 + b^2 \le 2 and A2+B2≤1A^2 + B^2 \le 1.

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