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

Question

6837 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-07-12T11:22:06

You can use the identity:
$sin^2(x)+cos^2(x)=1$
with:
$sin^2(x)=1-cos^2(x)$

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

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