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pre cal

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simplify sin (8x) using only sin(x) and cos (x)

  • pre cal -

    sin8x = 2sin4xcos4x
    = 4sin2xcos2x(cos^2(2x)-sin^2(2x))
    = 8sinx*cosx(cos^2(x)-sin^2(x))[(cos^2(x)-sin^2(x)]^2 - 4sin^2(x)cos^2(x)]

    and you can expand that in many ways, one of which is, using s=sin(x) c=cos(x):

    8sc^7 - 56s^3c^5 + 56s^3c^5 - 8s^7c

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