SOLUTION: Hello, The problem that I have is that I need to verify the identity: sin^4x+cos^4x=1-2cos^2x+2cos^4x I started with the right hand side and I tried to group the two co

Question 635024: Hello,
The problem that I have is that I need to verify the identity:
sin^4x+cos^4x=1-2cos^2x+2cos^4x
I started with the right hand side and I tried to group the two cosine identities
=1-2cos^2x+2cos^4x
=1-2cos^2x(1-cos^2x)
using the Pythagorean identity I got
=1-2cos^2x(sin^2x)
I'm not sure if I can use the Pythagorean identity on the first part making it
=(2sin^2x)(sin^2x)
But if I do, I'm not getting any closer to the left hand side.
Please help, or tell me if I'm at least on the right track.
Thank you
Found 2 solutions by richwmiller, MathTherapy:
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
You have cos^4x on both sides.
so subtracting it from both sides
sin^4x=1-2cos^2x+cos^4x
apparently this is a known identity.

Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!
Hello,
The problem that I have is that I need to verify the identity:
sin^4x+cos^4x=1-2cos^2x+2cos^4x
I started with the right hand side and I tried to group the two cosine identities
=1-2cos^2x+2cos^4x
=1-2cos^2x(1-cos^2x)
using the Pythagorean identity I got
=1-2cos^2x(sin^2x)
I'm not sure if I can use the Pythagorean identity on the first part making it
=(2sin^2x)(sin^2x)
But if I do, I'm not getting any closer to the left hand side.
Please help, or tell me if I'm at least on the right track.
Thank you

Since , then

We now have:

When the left-side is FOILED, you end up with the right-side.

OR

Since , then: becomes:

This means that , or

(TRUE PYTHAGOREAN IDENTITY)

Send comments and �thank-yous� to �D� at MathMadEzy@aol.com
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