If the equation has a real solution

MATHEMATICS · Single correct · A Level · Mathematics · Trigonometry · Trigonometry

Problem

If the equation asin⁡x+bcos⁡(x+θ)+bcos⁡(x−θ)=da\sin x+b\cos(x+\theta)+b\cos(x-\theta)=d has a real solution, then the minimum value of ∣cos⁡θ∣|\cos\theta| is (1) 12∣b∣d2−a2\frac{1}{2|b|}\sqrt{d^2-a^2} (2) 12∣a∣d2−a2\frac{1}{2|a|}\sqrt{d^2-a^2} (3) 12∣d∣d2−a2\frac{1}{2|d|}\sqrt{d^2-a^2} (4) None of these

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