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If $a \cos x + b \cos 3 x \leq 1 \forall x \in R, t h e n |b|$

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is equal to 1

≤1

≥1

None of these

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detailed solution

Correct option is B

Given acosx+bcos3x≤1For x=0, a+b≤1→i for x=π3, a2−b≤1→iifor x=2π3, -a2+b≤1→iiiand for x=π, −a−b≤1→ivFrom (i) and (iii) b≤1 and from (ii) and (iv) −b≤1⇒-1≤b≤1⇒b≤1

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If acosx+bcos3x≤1 ∀x∈R, then b

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If $a \cos x + b \cos 3 x \leq 1 \forall x \in R, t h e n |b|$