SOLUTION: (cos2x+sin2x)^2=1+sin4x

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Question 1130401: (cos2x+sin2x)^2=1+sin4x
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

%28cos%282x%29%2Bsin%282x%29%29%5E2=1%2Bsin%284x+%29
cos%5E2%282x%29%2B2cos%282x%29sin%282x%29%2Bsin%5E2%282x%29=1%2Bsin%284x+%29
Double Angle Identities
sin%282x%29+=+2+sin%28x%29+cos%28x%29,->sin%5E2%282x%29=%281%2F2+%29sin%284x%29
cos%282x%29+=+cos%5E2%28x%29+-+sin%5E2%28x%29->cos%5E2%282x%29=%281%2F2%29+%28cos%284x%29+%2B+1%29





%281%2F2%29+%28+2+%29%2B+sin%284x%29=1%2Bsin%284x+%29
1%2B+sin%284x%29=1%2Bsin%284x%29

Answer by ikleyn(52817) About Me  (Show Source):
You can put this solution on YOUR website!
.
cos%282x%29+%2B+sin%282x%29%29%5E2 = cos%5E2%282x%29+%2B+2%2Acos%282x%29%2Asin%282x%29+%2B+sin%5E2%282x%29 = %28cos%5E2%282x%29+%2B+sin%5E2%282x%29%29 + 2%2Acos%282x%29%2Asin%282x%29 = 1 + 4*sin(2x).

Completed, proved and solved.