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# Hard OCR CORE 4 Proof watch

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1. Hi guys!

Okay I can't do this question, and have spent the last 2 hours on it:/

1a) By first expressing Cos4x in terms of Cos2x, show that Cos4x=8cos^4 - 8 cos^2 +1

And hence show that 8 Cos^4x= Cos4x + 4Cos2x +3.

I don't know where to start tbh!
I tried using Cos(2x+2x) to get Cos2x.Cos2x - Sin2x.Sin2x
Therefore I get Cos4x- Sin4x... now I have no idea what do

2. But you've got the right idea. Use Pythagoras to get everything in terms of cos:

etc.

3. (Original post by J DOT A)
Hi guys!

Okay I can't do this question, and have spent the last 2 hours on it:/

1a) By first expressing Cos4x in terms of Cos2x, show that Cos4x=8cos^4 - 8 cos^2 +1

And hence show that 8 Cos^4x= Cos4x + 4Cos2x +3.

I don't know where to start tbh!
I tried using Cos(2x+2x) to get Cos2x.Cos2x - Sin2x.Sin2x
Therefore I get Cos4x- Sin4x... now I have no idea what do

The bolded line is a mistake.
.

Can you recall an identity that connects and ?

Spoiler:
Show
\sin ^2(2x) + \cos ^2(2x) = 1[/latex].

Then recall the expansion of cos2x and use the identity linking and to get it all in terms of .

For the next part, note that:

.

Can you see the expansion of 4cos 2x in there.
4. (Original post by BJack)
You really need to use "equivalent to" signs rather than "equal to". They have a subtle difference in meaning.
5. (Original post by Farhan.Hanif93)
You really need to use "equivalent to" signs rather than "equal to". They have a subtle difference in meaning.
Ahh thank you! I got the answer!
However, I don't know how to show that 8Cos^4x= Cos4x + 4cos2x +3

So rearranging you get 8Cos^4x = Cos4x + 8Cos^2x -1

Now I don't know what to do!
6. (Original post by Farhan.Hanif93)
You really need to use "equivalent to" signs rather than "equal to". They have a subtle difference in meaning.
Not to a chemist!
7. (Original post by BJack)
Not to a chemist!
Sounds like a reasonable excuse to me. I'll let you off.

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Updated: March 16, 2011
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