document.write( "Question 880940: Which identity is not used in the proof of the identity 1 + cot^2(theta) = csc^2(theta)? \n" ); document.write( "
Algebra.Com's Answer #531858 by Edwin McCravy(20065)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"1\"\"%22%22%2B%22%22\"\"cot%5E2%28theta%29\" \"%22%22=%22%22\" \"csc%5E2%28theta%29\"\r\n" );
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document.write( "Here's the proof.\r\n" );
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document.write( "By the Pythagorean theorem, in any right triangle,\r\n" );
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document.write( "\"OPPOSITE%5E2\"\"%22%22%2B%22%22\"\"ADJACENT%5E2\" \"%22%22=%22%22\" \"HYPOTENUSE%5E2\"\r\n" );
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document.write( "Divide every term by \"OPPOSITE%5E2\"\r\n" );
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document.write( "\"OPPOSITE%5E2%2FOPPOSITE%5E2\"\"%22%22%2B%22%22\"\"ADJACENT%5E2%2FOPPOSITE%5E2\" \"%22%22=%22%22\" \"HYPOTENUSE%5E2%2FOPPOSITE%5E2\"\r\n" );
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document.write( "Use a rule of exponents\r\n" );
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document.write( "\"%28OPPOSITE%2FOPPOSITE%29%5E2\"\"%22%22%2B%22%22\"\"%28ADJACENT%2FOPPOSITE%29%5E2\" \"%22%22=%22%22\" \"%28HYPOTENUSE%2FOPPOSITE%29%5E2\"\r\n" );
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document.write( "Therefore\r\n" );
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document.write( "\"1\"\"%22%22%2B%22%22\"\"cot%5E2%28theta%29\" \"%22%22=%22%22\" \"csc%5E2%28theta%29\"\r\n" );
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document.write( "We only used the Pythagorean theorem and the definition of the trig\r\n" );
document.write( "ratios cotangent and cosecant.  There are many identities we did not need to use.\r\n" );
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document.write( "Edwin
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