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


by ku1005
Tags: cos4x, identities, simplify, sin4x, trigonometric
ku1005
ku1005 is offline
#1
Sep14-06, 01:59 AM
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!!!
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ku1005
ku1005 is offline
#2
Sep14-06, 02:04 AM
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!!
ku1005
ku1005 is offline
#3
Sep14-06, 02:05 AM
P: 66
got it guys*

LadyJ123
LadyJ123 is offline
#4
Dec1-07, 01:09 PM
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.
Dick
Dick is offline
#5
Dec1-07, 05:35 PM
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Thanks
P: 25,168
Quote Quote by LadyJ123 View Post
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.
Nice job LadyJ123. But in the future, don't post complete solutions to problems. Just give hints. It's in the forum rules.


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