document.write( "Question 1032966: Use the sum or difference identities to find the exact value of the trigonometric function.
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Algebra.Com's Answer #647589 by ikleyn(52798)\"\" \"About 
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document.write( "\"tan%2823pi%2F12%29\" = \"tan%28-pi%2F12%29\" = \"-tan%28pi%2F12%29\" = -tan(15°) = \"-sin%2815%5Eo%29%2Fcos%2815%5Eo%29\".\r\n" );
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document.write( "sin(15°) = \"sqrt%28%281-cos%2830%5Eo%29%29%2F2%29\" =   (formula of half argument for sine, see the lesson  Trigonometric functions of half argument  in this site)\r\n" );
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document.write( "= \"sqrt%28%281+-+sqrt%283%29%2F2%29%2F2%29\" = \"sqrt%28%282-sqrt%283%29%29%2F4%29\" = \"sqrt%282-sqrt%283%29%29%2F2\".\r\n" );
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document.write( "cos(15°) = \"sqrt%28%281%2Bcos%2830%5Eo%29%29%2F2%29\" =   (formula of half argument for sine, see the lesson  Trigonometric functions of half argument  in this site)\r\n" );
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document.write( "= \"sqrt%28%281+%2B+sqrt%283%29%2F2%29%2F2%29\" = \"sqrt%28%282%2Bsqrt%283%29%29%2F4%29\" = \"sqrt%282%2Bsqrt%283%29%29%2F2\".\r\n" );
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document.write( "Therefore,  tan(15°) = \"sqrt%282-sqrt%283%29%29%2Fsqrt%282%2Bsqrt%283%29%29\".\r\n" );
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document.write( "You can rationalize the denominator in the last expression by multiplying the numerator and the denominator by \"sqrt%282-sqrt%283%29%29\". You will get \r\n" );
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document.write( "tan(15°) = \"sqrt%282-sqrt%283%29%29%2Fsqrt%282%2Bsqrt%283%29%29\" =  = \"%282-sqrt%283%29%29%2Fsqrt%284-sqrt%283%29%5E2%29\" = \"2-sqrt%283%29\".\r\n" );
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document.write( "Finally,  \"tan%2823pi%2F12%29\" = \"-tan%2815%5Eo%29\" = \"-%282-sqrt%283%29%29\" = \"sqrt%283%29-2\"  (negative value).\r\n" );
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document.write( "It is your answer. The problem is solved.\r\n" );
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document.write( "See also the lesson  Trigonometric functions of half argument - Examples,  Example 2. \r\n" );
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