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    Cos3x Açılımı

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    December 12, 2023

    Cos3x Açılımı İspatı cos(3x) = cos(2x+x) cos(a+b) = cosa.cosb - sina.sinb cos(3x) = cos2x.cosx - sin2x.sinx cos2x = cos²x - sin²x = 2.cos²x - 1= 1 - 2.sin²x


    Cos3x_Açılımı


    Cos3x Açılımı İspatı


    cos(3x) = cos(2x+x)

    cos(a+b) = cosa.cosb - sina.sinb

    cos(3x) = cos2x.cosx - sin2x.sinx

    cos2x = cos²x - sin²x = 2.cos²x - 1= 1 - 2.sin²x

    sin2x =2.sinx.cosx

    cos(3x) = (2.cos²x - 1).cosx - 2.sinx.cosx.sinx

    cos(3x) = cosx.(2.cos²x - 1) - 2.sinx.cosx.sinx

    cos(3x) = 2.cos³x - cosx - 2.sin²x.cosx

    sin²x = 1 - cos²x

    cos(3x) = 2.cos³x - cosx - 2.(1 - cos²x).cosx

    cos(3x) = 2.cos³x - cosx - 2.cosx.(1 - cos²x)

    cos(3x) = 2.cos³x - cosx - 2.cosx + 2.cos³x

    cos(3x) = 2.cos³x + 2.cos³x - cosx - 2.cosx

    cos(3x) = 4.cos³x - 3.cosx olur.

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