document.write( "Question 1208309: 1/tan^2pie/8 - 1/sin^2pie/8\r
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Algebra.Com's Answer #846648 by ikleyn(52879) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( " I will evaluate an expression $\"1%2Ftan%5E2%28x%29\"$ - $\"1%2Fsin%5E2%28x%29\"$ for arbitrary x =/= 0, +/- $\"pi\"$ , +/- $\"2pi\"$ , . . . \r
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document.write( "We have  } = .\r\n" );
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document.write( "THEREFORE,   -  =  -  = .\r\n" );
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document.write( "The numerator is  , by Pythagoras.  THEREFORE, the last fraction in the previous line is -1.\r\n" );
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document.write( "ANSWER.  The expression   -   is identically equal to -1 \r\n" );
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document.write( "         for all values of x different from 0, +/-, +/-, . . . \r\n" );
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document.write( "         In particular,   -   is -1.\r\n" );
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