document.write( "Question 659671: I have to verify the identity of
\n" ); document.write( "(1+sin(alpha))(1-sin(alpha))=cos^2(alpha) \n" ); document.write( "

Algebra.Com's Answer #410868 by DrBeeee(684) $\"\"$ $\"About$

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Start with the well known identity (you can easily prove it)
\n" ); document.write( "(1) sin^2(x) + cos^2(x) = 1
\n" ); document.write( "Now subtract sin^2(x) from each side and get
\n" ); document.write( "(2) cos^2(x) = 1 - sin^2(x)
\n" ); document.write( "Now factor the right side using the property
\n" ); document.write( "(3) (a^2-b^2) = (a+b)*(a-b), called the difference of two perfect squares in algebra (remember?), and get
\n" ); document.write( "(4) cos^2(x) = (1+sin(x))*(1-sin(x)) QED
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