trig

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By expressing 3x as (2x + x) prove that
cos3x = 4cos^3x - 3cosx

  • trig -

    cos(3x)
    = cos(2x + x)
    = cos2xcosx - sin2xsinx
    = (2cos^2 x -1)cosx - (2sinxcosx)sinx
    = 2cos^3 x - cosx - 2sin^2 x (cosx)
    = 2 cos^3x - cosx - 2(1 - cos^2 x)(cosx)
    = 2 cos^3x - cosx - 2cosx + 2cos^3x
    = 4cos^3x - 3cosx
    = RS

    Nice!

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