document.write( "Question 69609: How do I go about finding the exact value of tan(pi/4-pi/3)? \n" ); document.write( "
Algebra.Com's Answer #49580 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "How do I go about finding the exact value\r\n" );
document.write( "of \"tan%28pi%2F4-pi%2F3%29\"?\r\n" );
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document.write( "You have to know the formula \r\n" );
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document.write( "\"tan%28A-B%29=%28tan%28A%29-tan%28B%29%29%2F%281%2Btan%28A%29tan%28B%29%29\"\r\n" );
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document.write( "Substitute \"pi%2F4\" for A and \"pi%2F3\" for B:\r\n" );
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document.write( "Now you have to know that\r\n" );
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document.write( "\"tan%28pi%2F4%29+=+1\" and that \"tan%28pi%2F3%29=+sqrt%283%29\"\r\n" );
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document.write( "So substitute these:\r\n" );
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document.write( "\"tan%28pi%2F4-pi%2F3%29=%281-sqrt%283%29%29%2F%281%2B%281%29sqrt%283%29%29\"\r\n" );
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document.write( "or\r\n" );
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document.write( "\"tan%28pi%2F4-pi%2F3%29=%281-sqrt%283%29%29%2F%281%2Bsqrt%283%29%29\"\r\n" );
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document.write( "Your teacher may accept it that way, but s/he \r\n" );
document.write( "probably would prefer that you rationalize the \r\n" );
document.write( "denominator:\r\n" );
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document.write( "\"tan%28pi%2F4-pi%2F3%29=%281-2sqrt%283%29%2B3%29%2F%281-3%29\"\r\n" );
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document.write( "\"tan%28pi%2F4-pi%2F3%29=%284-2sqrt%283%29%29%2F%28-2%29\"\r\n" );
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document.write( "Factor 2 out of the numerator\r\n" );
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document.write( "\"tan%28pi%2F4-pi%2F3%29=%282%29%282-sqrt%283%29%29%2F%28-2%29\"\r\n" );
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document.write( "Cancel the \"-2\" in the bottom into the\r\n" );
document.write( "\"2\" in the top, getting -1 in the top:\r\n" );
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document.write( "\"tan%28pi%2F4-pi%2F3%29=+-1%282-sqrt%283%29%29\"\r\n" );
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document.write( "Remove the parentheses:\r\n" );
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document.write( "\"tan%28pi%2F4-pi%2F3%29=+-2%2Bsqrt%283%29\"\r\n" );
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document.write( "or you can save one sign by writing the\r\n" );
document.write( "second term first\r\n" );
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document.write( "\"tan%28pi%2F4-pi%2F3%29=+sqrt%283%29-2\"\r\n" );
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document.write( "Edwin
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