You are Here: Home >< Maths

# C3 Identify proof question

Announcements Posted on
Would YOU be put off a uni with a high crime rate? First 50 to have their say get a £5 Amazon voucher! 27-10-2016
1. I have no idea how I have messed up this identity proof question

Prove: Cos4x is identical to 8cos^(4)x-8cos^(2)x+1

I started with the left hand side, rewriting it as

Cos(2x+2x)

I then used the compound formula to obtain

cos2xcos2x-sin2xsin2x

Using double angle formulae

(cos^(2)x-sin^(2)x)^(2) - (2sinxcosx)^2

Expanding the squared brackets to obtain

cos^(4)x-2cos^(2)xsin^(2)x+sin^(4)x+4sin^ (2)xcos^(2)x

Collecting like terms

sin^(4)x+cos^(4)x+2cos^(2)xsin^( 2)x

Using the identity sin^(2)x = 1-cos^(2)x and expanding the bracket

sin^(4)x+cos^(4)x+2cos^(2)x-2cos^(4)x

Collecting like terms again

sin^(4)x-cos^(4)x+2cos^(2)x

Using the identity sin^(4)x = (1-cos^(2)x)^(2)

1-2cos^(2)x+cos^(4)x-cos^(4)x-2cos^(2)x

Collecting like terms for the last time cancels out the trig terms, leaving just...

1

I know this is a lot of workings, but can somebody please tell me where I've gone wrong?
2. (Original post by jamb97)
I have no idea how I have messed up this identity proof question

Prove: Cos4x is identical to 8cos^(4)x-8cos^(2)x+1

I started with the left hand side, rewriting it as

Cos(2x+2x)

I then used the compound formula to obtain

cos2xcos2x-sin2xsin2x

Using double angle formulae

(cos^(2)x-sin^(2)x)^(2) - (2sinxcosx)^2

Expanding the squared brackets to obtain

cos^(4)x-2cos^(2)xsin^(2)x+sin^(4)x+4sin^(2)xcos^(2)x
First error - in red - should be minus.

Not checked the rest.
3. (Original post by ghostwalker)
First error - in red - should be minus.

Not checked the rest.
But why? Surely if you square that you will get a positive...?

EDIT: Nevermind, I see what has gone wrong. I misinterpreted my own working... Thank you very much! :P

## Register

Thanks for posting! You just need to create an account in order to submit the post
1. this can't be left blank
2. this can't be left blank
3. this can't be left blank

6 characters or longer with both numbers and letters is safer

4. this can't be left empty
1. Oops, you need to agree to our Ts&Cs to register

Updated: April 20, 2016
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:
Today on TSR

Find out here

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read here first

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams