You are Here: Home >< Maths

Double angles watch

1. Hi again.

Right so the question is

By using the identity cos 2A = 1 - 2 sin^2 A show that cos 4x = 1 - 8 sin^2 x cos^2 x

I have put

cos 4x ---> cos (2x + 2x)

= 1 - 2 sin^2 x + 1 - 2 sin^2 x

= 2 - 4 sin^2 x

So where the hell have they got their 8 and cos^2 x from?? I tried using the identities for cos 2x that have cos^2x in but it hasn't got me much closer to the answer they want.

TSR mathematicians, help me please!!! And thank you in advance, you guys have helped me a lot this weekend
2. cos4x = 1 - 2sin^2(2x) is the first line they were looking for.

Can you see what to do next? Work on the sin2x term.
3. (Original post by HaNzY)
I have put

cos 4x ---> cos (2x + 2x)

= 1 - 2 sin^2 x + 1 - 2 sin^2 x
no, you have to substitute the "x"s with "2x"s

1 - 2sin^2(2x)
4. (Original post by HaNzY)
cos 4x ---> cos (2x + 2x)

= 1 - 2 sin^2 x + 1 - 2 sin^2 x
Eurgh, I just realised what you did here. You've assumed that cos(2x + 2x) = cos(2x) + cos(2x) which is very, very bad and big school boy error.

cos(2x + 2x) = cos(2x)cos(2x) - sin(2x)sin(2x)
5. Tip:

and you already have an expression for in the question...
6. (Original post by Swayum)
cos4x = 1 - 2sin^2(2x) is the first line they were looking for.

Can you see what to do next? Work on the sin2x term.
I did this (which came out with the right answer!!)

1 - 2 (2 sinx cosx)^2

1 - 2 x 4 sin^2x cos^2x

=1 - 8 sin^2x cos^2x !!

Is this right?? Or have I forged a connection lol?
7. Yup, that's right

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: January 17, 2010
Today on TSR

Thought he was 19... really he's 14

University open days

Wed, 25 Jul '18
2. University of Buckingham
Wed, 25 Jul '18
3. Bournemouth University
Wed, 1 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

Chat with other maths applicants