document.write( "Question 1051954: usa a sum or difference identity to find the exact value of the expression cos(5pi/12) \n" ); document.write( "
Algebra.Com's Answer #667393 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
   \r\n" );
document.write( "\r\n" );
document.write( "\"5pi%2F12\" is not a special angle.  We see if we \r\n" );
document.write( "can break \"5pi%2F12\" into a sum or difference of \r\n" );
document.write( "the three special angles \"pi%2F4\", \"pi%2F6\", \r\n" );
document.write( "and \"pi%2F3\".\r\n" );
document.write( "\r\n" );
document.write( "We change the special angles so as to have denominator 12:\r\n" );
document.write( "\r\n" );
document.write( "\"pi%2F4\"\"%22%22=%22%22\"\"3pi%2F12\", \"pi%2F6\"\"%22%22=%22%22\"\"2pi%2F12\", \"pi%2F3\"\"%22%22=%22%22\"\"4pi%2F12\"\r\n" );
document.write( "\r\n" );
document.write( "So we see that \"pi%2F4%2Bpi%2F6\"\"%22%22=%22%22\"\"3pi%2F12%2B2pi%2F12\"\"%22%22=%22%22\"\"5pi%2F12\"\r\n" );
document.write( "\r\n" );
document.write( "We use the identity: \"cos%28alpha%2Bbeta%29\"\"%22%22=%22%22\"\"cos%28alpha%29cos%28beta%29-sin%28alpha%29sin%28beta%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"cos%285pi%2F12%29\"\"%22%22=%22%22\"\"cos%28pi%2F4%2Bpi%2F6%29\"\"%22%22=%22%22\"\"cos%28pi%2F4%29cos%28pi%2F6%29-sin%28pi%2F4%29sin%28pi%2F6%29\"\"%22%22=%22%22\"\r\n" );
document.write( "\r\n" );
document.write( "\"%28sqrt%282%29%2F2%29%28sqrt%283%29%2F2%29-%28sqrt%282%29%2F2%29%281%2F2%29\"\"%22%22=%22%22\"\"sqrt%286%29%2F4-sqrt%282%29%2F4\"\"%22%22=%22%22\"\"%28sqrt%286%29-sqrt%282%29%29%2F4\"\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );