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

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

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Answer 1 · 2015-11-15T17:08:18

$cos^4x$ - $sin^4x$
$(cos^2x)^2 - (sin^2)^2$
$(cos^2x+ sin^2x)(cos^2x - sin^2x)$ --applying the formula of $a^2 - b^2$
$1 × (cos^2x - sin^2x)$ --- since $cos^2x+sin^2x$ =1
$cos^2x - sin^2x$

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

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