2cosy=x+1/x,prove that cos2y=1/2(x^2+1/x^2)

Question

2cosy=x+1/x,prove that cos2y=1/2(x^2+1/x^2)

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Jasmine 1 month 2021-09-17T09:31:15+00:00 1 Answer 0 views 0

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    2021-09-17T09:32:23+00:00

    Answer:

    Step-by-step explanation:

    2Cosy = x + 1/x

    Square on both sides

    4Cos²y = (x + 1/x)²

    4Cos²y = x² + 1/x² + 2

    4Cos²y – 2 = x² + 1/x²

    2(2Cos²y – 1) = x² + 1/x²

    2Cos²y – 1 = 1/2[ x² + 1/x²]

    Cos2y = 1/2[x² + 1/x²]   (∵  Cos2θ = 2Cos²θ – 1)

    Hence proved.

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