document.write( "Question 1134076: cos(x+y)cos(x-y)=
\n" ); document.write( "
\n" ); document.write( "

Algebra.Com's Answer #751391 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "Use the two identities:\r\n" );
document.write( "\r\n" );
document.write( "\"cos%28x%2By%29+=+cos%28x%29cos%28y%29-sin%28x%29sin%28y%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"cos%28x-y%29+=+cos%28x%29cos%28y%29%2Bsin%28x%29sin%28y%29\"\r\n" );
document.write( "\r\n" );
document.write( "Multiply left sides and right sides:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Multiply out the right side \r\n" );
document.write( "\r\n" );
document.write( "\"cos%5E2%28x%29cos%5E2%28y%29-sin%5E2%28x%29sin%5E2%28y%29=%22%22\"\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\"cos%5E2%28x%29-sin%5E2%28y%29\" <-- possible final answer\r\n" );
document.write( "\r\n" );
document.write( "That may be far enough for your teacher, but you can keep \r\n" );
document.write( "going if you desire.  Use these two identities:\r\n" );
document.write( "\r\n" );
document.write( "\"cos%282x%29=2cos%5E2%28x%29-1\" and \"cos%282y%29=1-2sin%5E2%28y%29\"\r\n" );
document.write( "\r\n" );
document.write( "Solve them for the squared terms.\r\n" );
document.write( "\r\n" );
document.write( "\"2cos%5E2%28x%29=1%2Bcos%282x%29\" and \"2sin%282y%29=1-cos%5E2%28y%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"cos%5E2%28x%29=1%2F2%2Bexpr%281%2F2%29cos%282x%29\" and \"sin%282y%29=1%2F2-expr%281%2F2%29cos%5E2%28y%29\"\r\n" );
document.write( "\r\n" );
document.write( "Substitute in\r\n" );
document.write( "\r\n" );
document.write( "\"cos%5E2%28x%29-sin%5E2%28y%29=%22%22\"\r\n" );
document.write( "\r\n" );
document.write( "\"%281%2F2%2Bexpr%281%2F2%29cos%282x%29%29-%281%2F2-expr%281%2F2%29cos%282y%29%29=%22%22\"\r\n" );
document.write( "\r\n" );
document.write( "\"1%2F2%2Bexpr%281%2F2%29cos%282x%29-1%2F2%2Bexpr%281%2F2%29cos%282y%29=%22%22\"\r\n" );
document.write( "\r\n" );
document.write( "\"expr%281%2F2%29cos%282x%29%2Bexpr%281%2F2%29cos%282y%29=%22%22\"\r\n" );
document.write( "\r\n" );
document.write( "\"expr%281%2F2%29%28cos%282x%29%5E%22%22%2Bcos%282y%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );