Jase Bentley

2022-12-31

How to simplify $\mathrm{sin}\theta {\mathrm{cos}}^{2}\theta -\mathrm{sin}\theta$?

mercerizoblx

Expert

Remember that
$XXX{\mathrm{sin}}^{2}\left(\theta \right)+{\mathrm{cos}}^{2}\left(\theta \right)=1$
or (in a modified form)
$XXX{\mathrm{cos}}^{2}\left(\theta \right)-1=-{\mathrm{sin}}^{2}\left(\theta \right)$
Considering the expression:
$XXX\mathrm{sin}\left(\theta \right){\mathrm{cos}}^{2}\left(\theta \right)-\mathrm{sin}\left(\theta \right)$
we can factor this as
$XXX\mathrm{sin}\left(\theta \right)\cdot \left({\mathrm{cos}}^{2}\left(\theta \right)-1\right)$
The using the earlier identity, we have
$XXX\mathrm{sin}\left(\theta \right)\cdot \left(-\mathrm{sin}\left(\theta \right)\right)$
or
$XXX-{\mathrm{sin}}^{2}\left(\theta \right)$

Do you have a similar question?