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

by ku1005
Tags: cos4x, identities, simplify, sin4x, trigonometric
 P: 66 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!!!
 P: 66 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!!
 P: 66 got it guys*
P: 1

## Trigonometric Identities- simplify 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.
HW Helper