trig--power reducing formulas

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Having trouble with this problem:

Rewrite the expression as an equivalent expression that does not contain powers greater than 1.


Cos³x

My answer: cos³x=(cos²x)(cosx)

=(1+cos2x/2)(cosx)-->cos+cos³x/2...which is wrong

  • trig--power reducing formulas -

    You have to use doubling formulas again to express it in terms of cos(3x). If you know about complex numbers then the derivation is easy:

    cos(x) = [exp(i x) + exp(-i x)]/2

    cos^3(x) = 1/8 [exp(3 i x) +
    exp(-3 i x)+ 3 exp(ix) + 3 exp(-ix) ] =

    1/4 cos(3 x) + 3/4 cos(x)

  • trig--power reducing formulas -

    (cosx)+(cosx)(cosx)

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