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Rajan@2021
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If (2sinθ+3cosθ)=2, prove that (3sinθ-2cosθ)=±3

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This is the basic and exam oriented question from trigonometric identities in which we have given that (2sinθ+3cosθ)=2, and we need to prove that (3sinθ-2cosθ)=±3

Kindly give me a detailed solution of this question

RS Aggarwal, Class 10, chapter 13B, question no 10

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  1. Given 2sinθ + 3cosθ = 2

    Now

    (3sinθ2cosθ

    =(9sin²θ23sinθ2cosθ+4cos²θ

    =99cos²θ23cosθ2sinθ+44sin²θ

    =13−[(3cosθ+23cosθ2sinθ+(2sinθ)²]

    =13(2sinθ+3cosθ

    =13= 9

    So

    (3sinθ2cosθ= 9

    3sinθ2cosθ = ±9

    = ±3

     

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