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

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Answer 1 · 2015-05-07T19:29:57

Use the identities:

$a^2 - b^2 = (a - b)(a + b))$
$cos^2 x + sin^2 x = 1$

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

How do you prove sin^4x-cos^4x=sin^2x-cos^2xsin^4x-cos^4x=sin^2x-cos^2x?