Question

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

Answer 1

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

Explanation:

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)`