document.write( "Question 1099317: please could you verify this? \"%28tan%285x%2F2%29%29%2F%28tan%28x%2F2%29%29+=+%28sin3x%2Bsin2x%29%2F%28sin3x-sin2x%29\"This is where I got stuck. \n" ); document.write( "
Algebra.Com's Answer #713759 by Edwin McCravy(20064)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "To prove:\r\n" );
document.write( "\r\n" );
document.write( "\"%28tan%285x%2F2%29%29%2F%28tan%28x%2F2%29%29\"\"%22%22=%22%22\"\"%28sin%283x%29%2Bsin%282x%29%29%2F%28sin%283x%29-sin%282x%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "Work with left side:\r\n" );
document.write( "\r\n" );
document.write( "\"tan%285x%2F2%29\"\"%22%F7%22\"\"tan%28x%2F2%29\"\r\n" );
document.write( "\r\n" );
document.write( "Change to sines and cosines:\r\n" );
document.write( "\r\n" );
document.write( "\"%28sin%285x%2F2%29%29%2F%28cos%285x%2F2%29%29\"\"%22%F7%22\"\"%28sin%28x%2F2%29%29%2F%28cos%28x%2F2%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "Invert and multiply\r\n" );
document.write( "\r\n" );
document.write( "\"%28sin%285x%2F2%29%29%2F%28cos%285x%2F2%29%29\"\"%22%22%2A%22%22\"\"%28cos%28x%2F2%29%29%2F%28sin%28x%2F2%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"%28sin%285x%2F2%29cos%28x%2F2%29%29%2F%28cos%285x%2F2%29sin%28x%2F2%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"%28sin%285x%2F2%29cos%28x%2F2%29%5E%22%22%29\"\"%22%F7%22\"\"%28cos%285x%2F2%29sin%28x%2F2%29%5E%22%22%29\"\r\n" );
document.write( "\r\n" );
document.write( "Use a 'product to sum' formula, which is:\r\n" );
document.write( "\r\n" );
document.write( "         \"sin%28A%29cos%28B%29\"\"%22%22=%22%22\"\"expr%281%2F2%29%28sin%28A%2BB%29%5E%22%22%2Bsin%28A-B%29%29\"\r\n" );
document.write( "         [That's easy to prove using the formulas for sin(AħB)]\r\n" );
document.write( "\r\n" );
document.write( "\"expr%281%2F2%29%28sin%285x%2F2%2Bx%2F2%29%5E%22%22%2Bsin%285x%2F2-x%2F2%29%29\"\"%22%F7%22\"\"expr%281%2F2%29%28sin%28x%2F2%2B5x%2F2%29%5E%22%22%2Bsin%28x%2F2-5x%2F2%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"expr%281%2F2%29%28sin%286x%2F2%29%5E%22%22%2Bsin%284x%2F2%29%29\"\"%22%F7%22\"\"expr%281%2F2%29%28sin%286x%2F2%29%5E%22%22%2Bsin%28-4x%2F2%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"expr%281%2F2%29%28sin%283x%29%5E%22%22%2Bsin%282x%29%29\"\"%22%F7%22\"\"expr%281%2F2%29%28sin%283x%29%5E%22%22%2Bsin%28-2x%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "Use the \"odd-even\" identity sin(-A) = -sin(A)\r\n" );
document.write( "\r\n" );
document.write( "\"expr%281%2F2%29%28sin%283x%29%5E%22%22%2Bsin%282x%29%29\"\"%22%F7%22\"\"expr%281%2F2%29%28sin%283x%29%5E%22%22-sin%282x%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\"%28sin%283x%29%5E%22%22%2Bsin%282x%29%29%2F%28sin%283x%29%5E%22%22-sin%282x%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "Edwin
AKA AnlytcPhil
\n" ); document.write( "
\n" );