document.write( "Question 1042158: Hi i have to solve this problem, thanks for help.\r
\n" ); document.write( "\n" ); document.write( "Sin^4x - Cos^4x = Sin^2x - Cos^2x
\n" ); document.write( "

Algebra.Com's Answer #657106 by ikleyn(52797)\"\" \"About 
You can put this solution on YOUR website!
.
\n" ); document.write( "Hi i have to solve this problem, thanks for help.\r
\n" ); document.write( "\n" ); document.write( "Sin^4x - Cos^4x = Sin^2x - Cos^2x
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\r\n" );
document.write( "Are you familiar with this identity: \"a%5E2+-+b%5E2\" = {a+b)*(a-b)?\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "If not, or if you are not sure, look into the lesson The difference of squares formula in this site.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "OK. Now, apply this identity to the left side. You will get\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\"Sin%5E4%28x%29+-+Cos%5E4%28x%29\" = \"%28sin%5E2%28x%29+%2B+cos%5E2%28x%29%29%2A%28sin%5E2%28x%29+-+cos%5E2%28x%29%29\".\r\n" );
document.write( "\r\n" );
document.write( "But the first parentheses,  \"%28sin%5E2%28x%29+%2B+cos%5E2%28x%29%29\" is equal to 1, as everybody knows.\r\n" );
document.write( "\r\n" );
document.write( "Therefore, \r\n" );
document.write( "\r\n" );
document.write( "\"Sin%5E4%28x%29+-+Cos%5E4%28x%29\" = \"sin%5E2%28x%29+-+cos%5E2%28x%29\".\r\n" );
document.write( "\r\n" );
document.write( "QED.\r\n" );
document.write( "

\n" ); document.write( "
\n" ); document.write( "
\n" );