Bit of help with a question (1 Viewer)

[Starcraftmazter]

Hello there.

This is my first post on these forums, I can't remember how I found them 2 days ago, but anyway.

I have a Maths 3u Project due this Friday, and there's this one question - or rather part of a question I completely forgot about.


Anyway, part 3 of this question defies my logic. When working it out, I got the right answer, all except for a minus where there is meant to be a plus. I also subed Alpha = 30 just for the heck of it, and got 2 different things on each side of this equation, but the paper cannot be wrong, so...maybe someone here can shed some light on this.

I scanned the necessary writing, for everyone's convenience.

Question 8

Parts 1 & 2

Part 3
Note about my working out in part 3, I factored out the LHS of part 2 straight away, and didn't even bother writing it, for the sake of simplicity.

Then I just put it's final result ( 2+Sin 2Alpha) in the second last line. I hope this makes sense.


So, hope someone can...enlighten me.
Please

 

[vafa]

how sould i view this attachments?
do i need to register myself?

 

[Starcraftmazter]

What? You just click on the link, and they show up, no need to register anywhere.

 

[Riviet]

how sould i view this attachments?
do i need to register myself?

Scroll down.

 

[vafa]

you are right, you should have minus not plus

 

[Starcraftmazter]

So, are you certain the question is wrong?

That's why I posted this here, this thing actually counts for 25% or so ( can't remember for sure) of my yearly extension 1 mark, so you would think it would be right, but it doesn't appear to be.

 

[SoulSearcher]

I've got 4 - sin²2@, but for some reason now I can't see your links, and I can't remember what the answer was.

 

[vafa]

I did it myself, and yes you are absolutely right.View attachment 13511

 

[Riviet]

edit: sorry, my solution was wrong.

edit 2: how would you go about using part ii) to prove it though?

 

[SoulSearcher]

Problem there Riviet is that cos⁴x + sin⁴x does not equal 1, but rather 1 - 2cos²xsin²x

 

[Starcraftmazter]

Alright, thanks for your help guys, greatly appreciated.

btw. It's good to finally find an Australian forum for these things....there are too many US ones.

 

[SoulSearcher]

Here's how I would go about using part ii) for the answer.

4cos⁶x-4sin⁶x/cos²x-sin²x
= 4(cos⁶x-sin⁶x)/cos²x-sin²x
= 2(cos³x-sin³x)/cosx-sinx * 2(cos³x+sin³x)/cosx+sinx
= (2+sin2x)(2-sin2x) [Note here that I skipped showing that 2(cos³x+sin³x)/cosx+sinx = 2-sin2x]
= 4 - sin²2x