document.write( "Question 235431: please prove: \"%28sin%28x%29%2Bsin%283x%29%29%2F%28cos%28x%29%2Bcos%283x%29%29=tan%282x%29\" \n" ); document.write( "
Algebra.Com's Answer #173432 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
\"%28sin%28x%29%2Bsin%283x%29%29%2F%28cos%28x%29%2Bcos%283x%29%29=tan%282x%29\"
\n" ); document.write( "
\r\n" );
document.write( "Work with only the left side:\r\n" );
document.write( "\r\n" );
document.write( "Write \"x\" as \"2x-x\" and \"3x\" as \"2x%2Bx\"\r\n" );
document.write( "\r\n" );
document.write( "\"%28sin%282x-x%29%2Bsin%282x%2Bx%29%29%2F%28cos%282x-x%29%2Bcos%282x%2Bx%29%29=tan%282x%29\"\r\n" );
document.write( "\r\n" );
document.write( "Use the identities\r\n" );
document.write( "\"sin%28alpha-beta%29=+sin%28alpha%29cos%28beta%29-cos%28alpha%29sin%28beta%29\"\r\n" );
document.write( "and \r\n" );
document.write( "\"sin%28alpha%2Bbeta%29=+sin%28alpha%29cos%28beta%29%2Bcos%28alpha%29sin%28beta%29\"\r\n" );
document.write( "to rewrite the numerator and\r\n" );
document.write( "use the identities \r\n" );
document.write( "\"cos%28alpha-beta%29=+cos%28alpha%29cos%28beta%29%2Bsin%28alpha%29sin%28beta%29\"\r\n" );
document.write( "and\r\n" );
document.write( "\"cos%28alpha%2Bbeta%29=+cos%28alpha%29cos%28beta%29-sin%28alpha%29sin%28beta%29\"\r\n" );
document.write( "\r\n" );
document.write( "to rewrite the denominator \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Remove the parentheses\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Cancel:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The two terms on top are like terms, and\r\n" );
document.write( "the two terms on the bottom are also like terms\r\n" );
document.write( "\r\n" );
document.write( "\"%0D%0A%282sin%282x%29cos%28x%29+%29%2F%0D%0A%282cos%282x%29cos%28x%29+%29\"\r\n" );
document.write( "\r\n" );
document.write( "Cancel the 2'a and the cosines:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\"sin%282x%29%2Fcos%282x%29\"\r\n" );
document.write( "\r\n" );
document.write( "Use identity \"sin%28phi%29%2Fcos%28phi%29=tan%28phi%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"tan%282x%29\"\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );