You are Here: Home >< Maths

# Induction proof Watch

1. On a past paper for my maths exam board (ccea northern ireland) i got this question:

Use induction to prove
2^(n + 1) sin x cos x cos (2x) cos (4x) … cos [2^(n)x] = sin [2^(n + 1)x]
where n is a non-negative integer.

i literally have no clue how to even start this, i think it might involve de moivre's theorem somehow. I looked at my mark scheme and it says to use n=0...
And please, baby steps. i have the general way of solving this already on a mark scheme, i just need it explained. For example, how do you know where one term stops and the next starts, and why do you use n=0 instead of n=1?

(the paper i got this off was CCEA, FP2, May/June 2010, Question 5)
2. hey, I've moved your thread to the maths forum, you'll get a better response here
3. Thanks! how did you do that? I'm new here so there's some things i'm just getting used to.
4. (Original post by mathboy64)
On a past paper for my maths exam board (ccea northern ireland) i got this question:

Use induction to prove
2^(n + 1) sin x cos x cos (2x) cos (4x) … cos [2^(n)x] = sin [2^(n + 1)x]
where n is a non-negative integer.

i literally have no clue how to even start this, i think it might involve de moivre's theorem somehow. I looked at my mark scheme and it says to use n=0...
And please, baby steps. i have the general way of solving this already on a mark scheme, i just need it explained. For example, how do you know where one term stops and the next starts, and why do you use n=0 instead of n=1?

(the paper i got this off was CCEA, FP2, May/June 2010, Question 5)

Intro to mathematical induction:
http://nrich.maths.org/4718

May help
5. (Original post by mathboy64)
On a past paper for my maths exam board (ccea northern ireland) i got this question:

Use induction to prove
2^(n + 1) sin x cos x cos (2x) cos (4x) … cos [2^(n)x] = sin [2^(n + 1)x]
where n is a non-negative integer.

i literally have no clue how to even start this, i think it might involve de moivre's theorem somehow. I looked at my mark scheme and it says to use n=0...
And please, baby steps. i have the general way of solving this already on a mark scheme, i just need it explained. For example, how do you know where one term stops and the next starts, and why do you use n=0 instead of n=1?

(the paper i got this off was CCEA, FP2, May/June 2010, Question 5)
You don't need de moivre's, it's a lot simpler than that. The reason why they use n=0 is because the principle of induction works wherever you start it. For example, if you started at n=5, assumed true for n=k and thus true for n=k+1 then the statement is true for all n >= 5 then you could do the cases n=0,1,2,3,4 separately. For some things, for example, this is obviously not valid for n=0 or n=1 so we start at n=2. It's possible here and makes most sense to start from n=0 because it should be quite common knowledge that 2sinxcosx=sin2x.

6. I'm geting the feeling this is wrong, and i must do:

But how would i know to do this? Would i just have to recognise the "," notice that if n=0, , and so only count the term on the L.H.S. until i see the
7. (Original post by mathboy64)

I'm geting the feeling this is wrong, and i must do:

But how would i know to do this? Would i just have to recognise the "," notice that if n=0, , and so only count the term on the L.H.S. until i see the
It is the latter, if you look at it, the only thing that changes on the LHS is cos(2^nx) so you keep 2^(n+1)sinx and as n increases, multiply by the required cos(x) then cos(x)cos(2x) then cos(x)cos(2x)cos(4x) etc.

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: December 24, 2010
Today on TSR

### Oxford interview invitations

When can you expect yours?

### Official Cambridge interview invite list

Discussions on TSR

• Latest
• ## See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams

## Groups associated with this forum:

View associated groups
Discussions on TSR

• Latest
• ## See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.