document.write( "Question 240826: please verify \"%28Sin%5E2x%29%2F%282-2Cos%28x%29%29+=+Cos%5E2\"\"%28x%2F2%29\" \n" ); document.write( "
Algebra.Com's Answer #176434 by Edwin McCravy(20062)\"\" \"About 
You can put this solution on YOUR website!
\"%28Sin%5E2x%29%2F%282-2Cos%28x%29%29+=+Cos%5E2\"\"%28x%2F2%29\"
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document.write( "We will work only with the left sides.\r\n" );
document.write( "Using the identity \"Sin%5E2phi%2BCos%5E2phi=1\", \r\n" );
document.write( "we have \"Sin%5E2phi=1-Cos%5E2phi\" and so we\r\n" );
document.write( "replace \"Sin%5E2x\" by \"1-Cos%5E2x\"\r\n" );
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document.write( "\"%281-Cos%5E2x%29%2F%282-2Cos%28x%29%29+=+Cos%5E2\"\"%28x%2F2%29\"\r\n" );
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document.write( "Factor the numerator as the difference perfect \r\n" );
document.write( "squares, and factor 2 out of the denominator:\r\n" );
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document.write( "\"%28+%281-Cos%28x%29%29%281%2BCos%28x%29%29%29%2F%282%281-Cos%28x%29%29%29+=+Cos%5E2\"\"%28x%2F2%29\"\r\n" );
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document.write( "Cancel the \"%281-Cos%28x%29%29\" factors:\r\n" );
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document.write( "\"%28x%2F2%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"1%2F2\"\"%281%2BCos%28x%29%29+=+Cos%5E2\"\"%28x%2F2%29\"\r\n" );
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document.write( "Now we use the identity \"Cos%282phi%29=2Cos%5E2phi-1\"\r\n" );
document.write( "by letting \"phi=x%2F2\".  This gives \"Cos%282%28x%2F2%29%29=2Cos%5E2\"\"x%2F2-1\"\r\n" );
document.write( "or \"Cos%28x%29=2Cos%5E2\"\"%28x%2F2%29-1\". So we substitute that\r\n" );
document.write( "for \"Cos%28x%29\"\r\n" );
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document.write( "\"1%2F2\"\"%22%28%22\"\"1%2B2Cos%5E2\"\"%28x%2F2%29-1+\"\"%22%29%22\"\"+%22%22+=+Cos%5E2\"\"%28x%2F2%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"1%2F2\"\"%22%28%22\"\"2Cos%5E2\"\"%28x%2F2%29\"\"%22%29%22\"\"+%22%22+=+Cos%5E2\"\"%28x%2F2%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"1%2Fcross%282%29\"\"%22%28%22\"\"cross%282%29Cos%5E2\"\"%28x%2F2%29\"\"%22%29%22\"\"+%22%22+=+Cos%5E2\"\"%28x%2F2%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"Cos%5E2\"\"%28x%2F2%29\"\"%22=%22\"\"Cos%5E2\"\"%28x%2F2%29\"\r\n" );
document.write( "\r\n" );
document.write( "Edwin
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