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

[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 can't seem to have 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!

 

[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!

 

[ku1005]

got it guys*

 

[LadyJ123]

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.

 

[Dick]

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.