# Math Help - verifying trig identities

1. ## verifying trig identities

Could someone please explain to me how to get through to the next step of verifying the identity?

$
cos^3 x sin^2 x = (sin^2 x - sin^4 x) cos x
$

$
cos x(sin^2 x - sin^4 x) =
$

$
cos x sin^2 x - sin^4 x cos x =
$

What Next?

2. Originally Posted by robasc
I am tyring to prove that:

$
cos^3 x sin^2 x
$

Equals:
$
(sin^2 x - sin^4 x) cos x
$
Prove $\cos^3 x \sin^2 x \equiv (\sin^2 x - \sin^4 x) \cos x$

Consider the LHS

$\cos^3 x \sin^2 x = \cos x \cos^2 x \sin^2 x$

$= \cos x (1 - \sin^2 x ) \sin^2 x$

$= \cdots$

3. Prove

Consider the LHS

__________________

So the next move would be:

$
cos x(1 - sin^2 x) sin^2 x =
$

$
cos x(sin^2 x - sin^4 x)
$

and that's it!