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Rajan@2021
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If acosθ+bsinθ = m and asinθ-bcosθ = n, prove that (m²+n²) = (a²+b²)

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Sir please give me a detailed solution of this question as it is taken from RS Aggarwal book in which we have been asked to prove that (m²+n²)=(a²+b²) and we have given that acosθ+bsinθ = m and asinθ-bcosθ = n

Book – RS Aggarwal, Class 10, chapter 13B, question no 1

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1 Answer

  1. acosθ+bsinθ=m
    Squaring equation, we get
    cos²θ+sin²θ+2abcosθ=....(1)

    Again square equation, asinθbcosθ=n
    sin²θ+cos²θ2abcosθsinθ=....(2)

    Add (1) and (2)
    cos²θ+sin²θ+2abcosθsinθ+sin²θ+cos²θ2abcosθsinθ
    =+
    (cos²θ+sin²θ)+(cos²θ+sin²θ)=+
    (Using cos²θ+sin²θ=1)
    +=+
    Hence proved.

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