document.write( "Question 22305: Explain why tan(x+450°) cannot be simplified using the tangent sum formulas but can be simplified by using he sine and cosine formulas? \n" ); document.write( "
Algebra.Com's Answer #11676 by AnlytcPhil(1810)\"\" \"About 
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Explain why tan(x+450°) cannot be simplified using the tangent sum \r\n" );
document.write( "formulas but can be simplified by using he sine and cosine formulas?\r\n" );
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document.write( "If we tried to use\r\n" );
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document.write( "tan(a+b) = (tana + tanb)/(1 - tana·tanb)\r\n" );
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document.write( "with a = x and b = 450°, then tanb would be tan450°, which\r\n" );
document.write( "is not defined.\r\n" );
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document.write( "However sin(a+b) = sina·cosb + cosa·sinb and\r\n" );
document.write( "        cos(a+b) = cosa·cosb - sina·sinb  \r\n" );
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document.write( "would only involve sin450° and cos450° which are defined\r\n" );
document.write( "respectively as 1 and 0,\r\n" );
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document.write( "then\r\n" );
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document.write( "sin(x+450°) = sinx·cos450°+cosx·sin450° = sinx·0+cosx·1 = cosx\r\n" );
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document.write( "and\r\n" );
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document.write( "cos(x+450°) = cosx·cos450°-sinx·sin450° = cosx·0-sinx·1 = -sinx\r\n" );
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document.write( "therefore\r\n" );
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document.write( "tan(x+450°) = sin(x+450°)/cos(x+450°) = cosx/(-sinx) =\r\n" );
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document.write( "-cosx/sinx = -cotx.\r\n" );
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document.write( "Edwin\r\n" );
document.write( "AnlytcPhil@aol.com
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