Thread: 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.

Originally Posted by iluvmathbutitshard

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

continue ...

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

Just in case, you should know this...



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

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 .

Grandad

Thank you so much.