Respostas

2013-10-20T21:21:48-02:00
Sen^4(x) - cos^4(x) = 
(sen^2(x) - cos^2(x) )(sen^2(x) + cos^2(x)) = 
(sen^2(x) - cos^2(x) )(1) = 
cos^2(x) - cos^2(x) =
2cos^2(x)
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2013-10-20T21:27:24-02:00
\sin^4x-\cos^4x=1-2\cos^2x\\\\
\sin^4x-\cos^4x=1-(\cos^2x+\cos^2x)\\\\
\sin^4x-\cos^4x=1-\cos^2x-\cos^2x\\\\
\sin^4x-\cos^4x=\sin^2x-\cos^2x\\\\
(\sin^2x+\cos^2x)(\sin^2x-\cos^2x)=\sin^2x-\cos^2x

Dividindo-se toda equação por \sin^2x-\cos^2x, temos:

\sin^2x+\cos^2=1\Longrightarrow OK!\;\blacksquare
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