# Trigonometric Identities- simplify sin^4x - cos^4x

1. Sep 14, 2006

### ku1005

hey just wonderin if any1 could give me a hint as to the best method to prove the following trigonometric indentity:

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

i tried the side more complicated first...but cant seem to hav any luck...other then maing it more complicated!!!

umm the x's are meant to be thetas...but didnlt ahv the symbol handy.and its meant to be read sign to he power 4 theta....really aprreciate any ideas for this one!!!

2. Sep 14, 2006

### ku1005

sorry got guys!!!...kool just factor out as 2 lots of sin^2theta...use pythagorean indentity to sub and then cancel like terms.....WORKS a charm lol...thanks if anyoe read tis anyways!!

3. Sep 14, 2006

### ku1005

got it guys*

4. Dec 1, 2007

How To Simplify and Prove: sin^4x-cos^4x

Given: sin^4x-cos^4x

(sin^2x-cos^2x)(sin^2x+cos^2x) Factoring
(1)(sin^2x-cos^2x) Pythagorean Identity
(1)(1-cos^2x-cos^2x) Pythagorean Identity
(1)(1-2cos^2x) Combine Like Terms
1-2cos^2x Multiply

Hope This Helps.

5. Dec 1, 2007

### Dick

Nice job LadyJ123. But in the future, don't post complete solutions to problems. Just give hints. It's in the forum rules.