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Rajan@2021
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If tanA=ntanB and sinA=msinB, prove that cos²A= (m²-1)/(n²-1)

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One of the most important and exam oriented question from trigonometry, topic – trigonometric identities in which we have given that tanA=ntanB and also sinA=msinB, we have to prove that cos²A= (m²-1)/(n²-1)

Kindly give me a detailed solution of this question

RS Aggarwal, Class 10, chapter 13B, question no 14

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  1. sinA=msinB(1)

    tanA=ntanB
    sinA/cosA = nsinB​/cosB(2)
    Substituting sinB from equation 1, we get
    cosB=n/m cosA(3)
    sin²A=sin²B

    1cos²A = (1cos²B)

    Substituting equation 3, we get

    1cos²A = (1cos²A),
    cos²A = (1)/(n²-1) (proved)

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