You are Here: Home >< Maths

# FP2 - Trigonometric identities watch

1. Hi!

Im finding trigonometric identities relatively hard, and Im wondering if anyone can help me solve the question below:

(X replaces THETA)

Code:
Show that 8Cos^4X = cos4X + 4cos2X + 3
Thanks!
2. Hi!

Im finding trigonometric identities relatively hard, and Im wondering if anyone can help me solve the question below:

(X replaces THETA)
Use this identity multiple times

Use this identity multiple times

I can't fault logic's method, but you did specify FP2.

Part of the FP2 idea is to be able to use De Moivre to expand cos(nx) or sin(nx). You then get some polynomial in cos and/or sin to play with.
4. (Original post by ian.slater)
I can't fault logic's method, but you did specify FP2.

Part of the FP2 idea is to be able to use De Moivre to expand cos(nx) or sin(nx). You then get some polynomial in cos and/or sin to play with.
Yeh!, I need to use De Moivre.

Can you help?
Thanks!
5. OK

exp(ix) = cos(x) + isin(x) by definition

so exp(nix) = (cos(x) + isin(x))^n

but also exp(nix) = cos(nx) + isin(nx)

If you expand say cos(4x) + isin(4x) = (cos(x) + isin(x))^4

you equate real parts to get cos(4x) and imag parts to get sin(4x).

Then the examiner dreams up ways to get you to use that
6. Yeh!, I need to use De Moivre.

Can you help?
Thanks!
Ah sorry did not know that. Ok then, De Moivre's theorem is

In your case i'd write this

Now expand the LHS and collect all the real terms, which will be equal to cos(4x)...
7. In the question, I'd use DM to expand cos(4x) (remembering that sin^2 = 1-cos^2) and also cos(2x) (although you could just quote that). Work out the RHS and hope when the smoke clears you're left with the LHS

### Related university courses

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: February 11, 2010
The home of Results and Clearing

### 2,679

people online now

### 1,567,000

students helped last year
Today on TSR

### Got into uni yesterday?

Come start a Freshers blog and win pizza!

### University open days

1. London Metropolitan University
Sat, 18 Aug '18
2. Edge Hill University
Sat, 18 Aug '18
3. Bournemouth University
Sat, 18 Aug '18
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