Sin3x Açılımı
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December 12, 2023
Sin3x Açılımı İspatı sin(3x) = sin(2x+x) sin(a+b) = sina.cosb + sinb.cosa sin(3x) = sin2x.cosx + sinx.cos2x sin2x =2.sinx.cosx cos2x = cos²x - sin²x = 2.cos
Sin3x Açılımı İspatı
sin(3x) = sin(2x+x)
sin(a+b) = sina.cosb + sinb.cosa
sin(3x) = sin2x.cosx + sinx.cos2x
sin2x =2.sinx.cosx
cos2x = cos²x - sin²x = 2.cos²x - 1= 1 - 2.sin²x
sin(3x) = 2.sinx.cosx.cosx + sinx.(1 - 2.sin²x)
sin(3x) = 2.sinx.cos²x + sinx - 2.sin³x
cos²x = 1 - sin²x
sin(3x) = 2.sinx.(1 - sin²x) + sinx - 2.sin³x
sin(3x) = 2.sinx - 2.sin³x + sinx - 2.sin³x
sin(3x) = 2.sinx + sinx - 2.sin³x - 2.sin³x
sin(3x) = 3.sinx - 4.sin³x olur.
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