Question

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

Answer 1

sin x cos^2x-sinx=sinx(cos^2x-1) <b>they took out a common factor of sinx</b>
=-sinx(1-cos^2x) <b>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 </b>
=-sinx(sin^2x) (Where does sine come from and what happend to cosine?)
=-sin^3x

<b> does it make sense now? </b>