# Trig question

1. Aug 1, 2011

### Saitama

1. The problem statement, all variables and given/known data
If sin x + sin2x + sin3x= 1, then find out the value of cos6x-4cos4x+8cos2x.

2. Relevant equations

3. The attempt at a solution
How should i start?
I don't find any way to convert them to cos 6x or cos 4x.

2. Aug 1, 2011

### SammyS

Staff Emeritus
Try using $\displaystyle \sin \theta + \sin \varphi = 2 \sin\left( \frac{\theta + \varphi}{2} \right) \cos\left( \frac{\theta - \varphi}{2} \right)$ to combine sin(x) + sin(3x) .

-- Just a possibility.

3. Aug 1, 2011

### Saitama

Using this identity i get:-
2sin2xcosx+sin2x=1

But what next?

4. Aug 2, 2011

### eumyang

I don't think the problem was copied correctly. I've seen this problem before. The numbers in front of the x's are supposed to be exponents, not multiples of angles.

The problem should be as follows:
If
$\sin x + \sin^2 x + \sin^3 x = 1$,
then find out the value of
$\cos^6 x - 4\cos^4 x + 8\cos^2 x$.

Here's a hint, and hopefully, it's not a big one:
Rewrite as
$\sin x + \sin^3 x = \cos^2 x$.
Then square both sides and use the identity
$\sin^2 x =1 - \cos^2 x$.
You should eventually get the answer.

Mods: if this is too big of a hint, then please delete.

5. Aug 2, 2011

### Saitama

You're right. I am very sorry for my foolishness. Please pardon me.