trigonometry

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Verify that following are identities:


1. cos 3t = 4 cos³ t-3 cos t

2. sin 4x = 8 sin x cos³ x-4 x cos x

(use a double-angle identity)

  • trigonometry -

    1.
    LS = cos 3t
    = cos(2t + t)
    = cos2tcost - sin2tsint
    = (2cos^2 t - 1)(cost) - 2sintcostsint
    = 2cos^3 t - cost - 2sin^2 t cost
    = 2cos^3 t - cost - 2(1 - cos^2 t)cost
    = 2cos^3 t - cost - 2cost + 2cos^3 t
    = 4cos^3 t - 3cost
    = RS

    for #2, start with
    LS = sin(2x + 2x)
    = sin2xcos2x + cos2x sin2x
    then use the double-angle formulas for each one
    simplify very carefully

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