SOLUTION: Prove sin^2 x cos^2 x + cos^4 x = (1-sinx) (1+sinx) is an identity

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Question 1159354: Prove sin^2 x cos^2 x + cos^4 x = (1-sinx) (1+sinx) is an identity
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Throughout this problem, I'm going to only alter the left side. The right side will stay the same the entire time.

sin%5E2%28x%29%2Acos%5E2%28x%29+%2B+cos%5E4%28x%29+=+%281-sin%28x%29%29%281%2Bsin%28x%29%29



Factor out the GCF cos^2(x)

cos%5E2%28x%29%281%29+=+%281-sin%28x%29%29%281%2Bsin%28x%29%29 Pythagorean Identity: sin^2(x) + cos^2(x) = 1

cos%5E2%28x%29+=+%281-sin%28x%29%29%281%2Bsin%28x%29%29

1-sin%5E2%28x%29+=+%281-sin%28x%29%29%281%2Bsin%28x%29%29 Variation of the pythagorean identity

%281-sin%28x%29%29%281%2Bsin%28x%29%29+=+%281-sin%28x%29%29%281%2Bsin%28x%29%29 Difference of squares rule

The identity has been confirmed as we get the same expression on both sides.