document.write( "Question 207450: find the exact value of tan 15degrees without using tables or a calculator \n" ); document.write( "
Algebra.Com's Answer #156870 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
Find the exact value of tan(15°) without using tables or a calculator
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document.write( "\"%2215%B0%22\" is not a special angle, however \"%2245%B0%22\" and \"%2230%B0%22\"\r\n" );
document.write( "are.  And \"%2215%B0%22=%2245%B0%22-%2230%B0%22\", so we can use this formula:\r\n" );
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document.write( "where \"alpha=%2245%B0%22\" and \"beta=%2230%B0%22\":\r\n" );
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document.write( "Multiply top and bottom by \"3\"\r\n" );
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document.write( "Rationalize the denominator:\r\n" );
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document.write( "Check by using your calculator.  \r\n" );
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document.write( "\"tan%28%2215%B0%22%29=+.2679491924\"\r\n" );
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document.write( "Then find the decimal value for\r\n" );
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document.write( "\"2-sqrt%283%29+=+.267941924\"\r\n" );
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document.write( "So it checks.\r\n" );
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document.write( "So the answer is \r\n" );
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document.write( "\"tan%28%2215%B0%22%29=2-sqrt%283%29\"\r\n" );
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document.write( "Edwin
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