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document.write( "First let's learn where the Pythagorean identities came from,\r\n" );
document.write( "namely the Pythagorean theorem:\r\n" );
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document.write( "
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document.write( "By the Pythagorean theorem:\r\n" );
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document.write( "
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document.write( "Divide through by
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document.write( "
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document.write( "
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document.write( "
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document.write( "That's the first Pythagorean identity:\r\n" );
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document.write( "-------------------------------------\r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "Divide through by
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document.write( "
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document.write( "
\r\n" );
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document.write( "
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document.write( "That's the second Pythagorean identity:\r\n" );
document.write( "\r\n" );
document.write( "-------------------------------------\r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "Divide through by
\r\n" );
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document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
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document.write( "
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document.write( "That's the third Pythagorean identity:\r\n" );
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document.write( "-------------------------------------\r\n" );
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document.write( "Be sure to memorize all three of them. Usually we write them\r\n" );
document.write( "this way, so they're easier to learn:\r\n" );
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document.write( "
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document.write( "
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document.write( "
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document.write( "--------------------------------------\r\n" );
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document.write( "Those identities are true for ALL angles
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document.write( "So for\r\n" );
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document.write( "



\r\n" );
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document.write( "Since the third Pythagorean identity\r\n" );
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document.write( "
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document.write( "is true for ALL angles
, let
, then\r\n" );
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document.write( "



\r\n" );
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document.write( "So we can replace 
by 
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document.write( "So your problem:\r\n" );
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document.write( "



\r\n" );
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document.write( "becomes:\r\n" );
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document.write( "



\r\n" );
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document.write( "then the \"cotangent squared\"s cancel:\r\n" );
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document.write( "



\r\n" );
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document.write( "and that just leaves 1, which is an integer.\r\n" );
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document.write( "Edwin
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document.write( "