How do you verify #sin x(1- 2 cos ^2 x + cos ^4 x) = sin ^5 x#?
The key to the proof is to factor the left hand side
When I see a set of parenthesis I always want to see if it can be factored into a simpler form.
So it turns out that
so our factored form is:
Now I see that we have
notice if we move the cosine to the other side then we have the
so let us substitute the
now it is just a matter of simplifying the left hand side.
and thus it is demonstrated.
and that makes us happy.