Math Help - Am I doing this wrong?

1. Am I doing this wrong?

I have to verify this identity algebraically:
sin x (1 - 2 cos^2 x + cos^4 x) = sin^5 x

So I have to make the left side equal the right,
My work so far:
sin x (sin^2 x cos^2 x + 4 coos x)
sin x (sin^2 x [1 - sin^2 x] + 4 cos^4 x)
sin x ([sin^2 x - sin^4 x] + 4 cos^4 x)
sin x ([sin^2 x + cos^4 x + 1] + 4 cos^4 x)
sin x (sin^2 x + 5 cos^4 x + 1)

Now I am stuck. Am I correct so far? If I am, what do I do next?
Any help is appreciated.

2. Originally Posted by iluvmathbutitshard
I have to verify this identity algebraically:
sin x (1 - 2 cos^2 x + cos^4 x) = sin^5 x

$
\sin{x}\textcolor{red}{(1 - \cos^2{x})^2} = \sin^5{x}
$
continue ...

3. sin x (1 - cos^2 x^2)^2
sin x (sin^2 x) (sin^2 x)
is this correct?

4. Just in case, you should know this...

$\sin^2\theta + \cos^2\theta = 1$

From this other things can be derived and it will help you with trig identities.

5. Hello iluvmathbutitshard
Originally Posted by iluvmathbutitshard
sin x (1 - cos^2 x^2)^2 You don't need the bit in red.
sin x (sin^2 x) (sin^2 x)
is this correct?
Yes, more or less (see above). And this, of course, gives $\sin^5x$.