# How do you verify cosx-cosxsin^2x=cos^3x?

Jul 12, 2015

You can use the identity:
${\sin}^{2} \left(x\right) + {\cos}^{2} \left(x\right) = 1$
with:
${\sin}^{2} \left(x\right) = 1 - {\cos}^{2} \left(x\right)$

#### Explanation:

You can write:
$\cos \left(x\right) - \cos \left(x\right) \left[1 - {\cos}^{2} \left(x\right)\right] = {\cos}^{3} \left(x\right)$
$\cos \left(x\right) - \cos \left(x\right) \cancel{+ {\cos}^{3} \left(x\right)} = \cancel{{\cos}^{3} \left(x\right)}$
rearranging:
$\cos \left(x\right) = \cos \left(x\right)$
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