How do you prove $cos^4 p - sin^4 p = cos 2 p$ ?

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Answer 1 · 2016-01-23T11:31:29

Use the difference of squares formula and double angle identity:
$cos^2x - sin^2x = cos2x$

$cos^4p - sin^4p = (cos^2p + sin^2p)(cos^2p-sin^2p)$

$= 1(cos^2p-sin^2p)$

$=cos2p$

How do you prove cos^4 p - sin^4 p = cos 2 pcos^4 p - sin^4 p = cos 2 p?