prove that sin4a+cos4a=1-2cos2a+2cos4a
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(sin^4a + cos^4a)
(sin^2a)^2 + (cos^2a)^2
(sin^2a+cos^2a)^2 - 2.sin^2a.cos^2a
1-2.sin2a.cos2a
1- 2.cos2a.(1-cos2a)
1+2cos4a-2.cos2a
(sin^2a)^2 + (cos^2a)^2
(sin^2a+cos^2a)^2 - 2.sin^2a.cos^2a
1-2.sin2a.cos2a
1- 2.cos2a.(1-cos2a)
1+2cos4a-2.cos2a
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