sin 4 A + cos 4 A = what
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cos 4a = cos 2(2a) =
cos^2 2a - sin^2 2a =
(cos^2 a - sin^2 a)^2 - (2 sin a cos a)^2 =
cos^4 a - 2 sin^2 a cos^2 a + sin^4 a - 4 sin^2 a cos^2 a =
cos^4 a + sin^4 a - 6 sin^2 a cos^2 a
cos^2 2a - sin^2 2a =
(cos^2 a - sin^2 a)^2 - (2 sin a cos a)^2 =
cos^4 a - 2 sin^2 a cos^2 a + sin^4 a - 4 sin^2 a cos^2 a =
cos^4 a + sin^4 a - 6 sin^2 a cos^2 a
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