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# Trig Identities watch

1. I've been asked to prove a trig identity. It involves cos 4x

Since sin is on the left hand side, I know I must use:

Cos 2x = 1 - 2sin²x

But how can i change it to cos 4x? I never learnt this is C3

Do you just square everything so it becomes:

cos 4x = 1-4sin^4 2x
2. Squaring would give you

Try
3. Say we have this:

Where A could be x or 2x...

Can you do it now?
4. If you replace x by 2x you obtain cos4x=1-2(sin2x)^2. Squaring everything doesn't give the expression you've written down.
5. (Original post by TheTallOne)
Say we have this:

Where A could be x or 2x...

Can you do it now?

(Original post by EierVonSatan)
Squaring would give you

Try

cos(A+B)=cos A cos B - sin A sin B

Therefore

Therefore:

Thus: ???
6. (Original post by djpailo)
Therefore:

Thus: ???
And remember:
7. I don't know where to go from there
8. What's the identity you're trying to prove?
9. So using your new formula for cos 4x and rewriting sin 2x = S you should be able to do it
10. (Original post by EierVonSatan)
So using your new formula for cos 4x and rewriting sin 2x = S you should be able to do it
Cool. I thought

was wrong lol. Okay, I'll try it out now.
11. I got it to:

but got stuck.

I could use sin^2...=1 but I don't think it'd get be anywhere :s

Edit: NVM! I found out where I went wrong. When I got rid of the outside the bracket, I carelessly let the 2 remain on . Thanks for all your help guys

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Updated: March 18, 2009
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