Trig

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Simplify sin x cos^2x-sinx

Here's my book's explanation which I don't totally follow

sin x cos^2x-sinx=sinx(cos^2x-1)
=-sinx(1-cos^2x)
=-sinx(sin^2x) (Where does sine come from and what happend to cosine?)
=-sin^3x

  • Trig -

    sin x cos^2x-sinx=sinx(cos^2x-1) they took out a common factor of sinx
    =-sinx(1-cos^2x) recall that sin^2x + cos^2x = 1, and then 1-cos^2x = sin^2x.
    Notice they had cos^2x-1 which is -(1-cos^2x). Also notice that there is now a - in front of the sinx

    =-sinx(sin^2x) (Where does sine come from and what happend to cosine?)
    =-sin^3x

    does it make sense now?

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