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Let $P = a \cos θ - b \sin θ$ Then for all real $θ$

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P>a2+b2

P<−a2+b2

−a2+b2≤P≤a2+b2

None of these

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detailed solution

Correct option is C

P=a2+b2aa2+b2cosθ+ba2+b2sinθ = a2+b2cosθ-α Where cosα=aa2+b2,sinα=ba2+b2 But −1≤cosθ-α≤1⇒- a2+b2≤ a2+b2cosθ-α≤a2+b2⇒- a2+b2≤ P≤a2+b2

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Let P=acosθ−bsinθ Then for all real θ

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Let $P = a \cos θ - b \sin θ$ Then for all real $θ$