document.write( "Question 1099479: Solve \"2cot%5E2%28x%29%2B3csc%28x%29=0\" given that 0 ≤ x < 2π \n" ); document.write( "
Algebra.Com's Answer #713902 by Edwin McCravy(20060)\"\" \"About 
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document.write( "\"2cot%5E2%28x%29%2B3csc%28x%29\"\"%22%22=%22%22\"\"0\"\r\n" );
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document.write( "Use the identity \"1%2Bcot%5E2%28theta%29\"\"%22%22=%22%22\"\"csc%5E2%28theta%29\"\r\n" );
document.write( "solved for cotangent2: \"cot%5E2%28theta%29\"\"%22%22=%22%22\"\"csc%5E2%28theta%29-1\"  \r\n" );
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document.write( "\"2%28csc%5E2%28x%29%5E%22%22-1%29%2B3csc%28x%29\"\"%22%22=%22%22\"\"0\"\r\n" );
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document.write( "\"2csc%5E2%28x%29-2%2B3csc%28x%29\"\"%22%22=%22%22\"\"0\"\r\n" );
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document.write( "\"2csc%5E2%28x%29%2B3csc%28x%29-2\"\"%22%22=%22%22\"\"0\"\r\n" );
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document.write( "Factor:\r\n" );
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document.write( "\"%28csc%28x%29%5E%22%22%2B2%29%282csc%28x%29%5E%22%22-1%29\"\"%22%22=%22%22\"\"0\"\r\n" );
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document.write( "\"csc%28x%29%2B2=0\"   \"2csc%28x%29-1=0\" \r\n" );
document.write( "\"csc%28x%29=-2\"   \"2csc%28x%29-1=0\"\r\n" );
document.write( "                  \"2csc%28x%29+=1\"\r\n" );
document.write( "                  \"csc%28x%29=1%2F2\"\r\n" );
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document.write( "Use the fact that cosecant is the reciprocal of the sine:\r\n" );
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document.write( "\"sin%28x%29=-1%2F2\"   \"sin%28x%29=2\"\r\n" );
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document.write( "The sine cannot be greater than 1 so we ignore sin(x)=2\r\n" );
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document.write( "\"matrix%281%2C5%2Cx%2C%22%22=%22%22%2C7pi%2F6%2C%22%2C%22%2C11pi%2F6%29\"\r\n" );
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document.write( "Edwin

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