Posted by **Tara** on Monday, January 4, 2010 at 9:06pm.

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 -
**Reiny**, Monday, January 4, 2010 at 9:19pm
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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