SOLUTION: Please proof that: sin^4x+cos^4x = 1-2sin^2xcos^2x

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Question 966196: Please proof that:
sin^4x+cos^4x = 1-2sin^2xcos^2x
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
sin%5E4%28x%29%2Bcos%5E4%28x%29%22%22=%22%221-2sin%5E2%28x%29cos%5E2%28x%29

(((sin^2(x)sin^2(x)+cos^2(x)cos^2(x)}}}

Substitute 1-cosē(x) for the second sinē(x) and
Substitute 1-sinē(x) for the first cosē(x)

(((sin^2(x)(1-cos^2(x))+(1-sin^2(x))cos^2(x)}}}

Distribute

sin%5E2%28x%29-sin%5E2%28x%29%2Bcos%5E2%28x%29-sin%5E2%28x%29cos%5E2%28x%29

Rearrange and group terms:

%28sin%5E2%28x%29%5E%22%22%2Bcos%5E2%28x%29%29-sin%5E2%28x%29-sin%5E2%28x%29

Substitute 1 for sinē(x)+cosē(x) and combine last two like terms.

1-2sin%5E2%28x%29cos%5E2%28x%29

Edwin