document.write( "Question 168554: I need help verifying these identities.
\n" ); document.write( "\"Sin%28x%29Cos%28x%29%2BCos%5E2x+=+Cos%28x%29%281%2BCot%28x%29%29%2FCsc%28x%29\"\r
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\n" ); document.write( "\n" ); document.write( "\"%28Sec%28x%29-Tan%28x%29%29%5E2+%2B+%28Sec%28x%29%2BTan%28x%29%29%5E2+=+2%2B4Tan%5E2x\"
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Algebra.Com's Answer #124270 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
): I need help verifying these identities.
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document.write( "\"Sin%28x%29Cos%28x%29%2BCos%5E2x+=+Cos%28x%29%281%2BCot%28x%29%29%2FCsc%28x%29\"\r\n" );
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document.write( "Work with the right \r\n" );
document.write( "side.  Substitute\r\n" );
document.write( "\"Cos%28x%29%2FSin%28x%29\"\r\n" );
document.write( "for \"Cot%28x%29\" and\r\n" );
document.write( "substitute \"1%2FSin%28x%29\"\r\n" );
document.write( "for \"Csc%28x%29\"\r\n" );
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document.write( "                      = \"%28Cos%28x%29%281%2BCos%28x%29%2FSin%28x%29%29%29%2F%281%2FSin%28x%29%29\"\r\n" );
document.write( "Distribute out the\r\n" );
document.write( "numerator:\r\n" );
document.write( "                      = \"+%28Cos%28x%29%2BCos%5E2x%2FSin%28x%29%29%2F%281%2FSin%28x%29%29\"\r\n" );
document.write( " \r\n" );
document.write( "Put a 1 under the \r\n" );
document.write( "\"Cos%28x%29\" so everything\r\n" );
document.write( "will be a fraction \r\n" );
document.write( "                      = \"+%28Cos%28x%29%2F1%2BCos%5E2x%2FSin%28x%29%29%2F%281%2FSin%28x%29%29\"\r\n" );
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document.write( "Invert the fraction\r\n" );
document.write( "in the denominator \r\n" );
document.write( "and multiply:\r\n" );
document.write( " \r\n" );
document.write( "                      = \"+%28Cos%28x%29%2F1%2BCos%5E2x%2FSin%28x%29+%29%2A%28+Sin%28x%29%2F1+%29\"\r\n" );
document.write( " \r\n" );
document.write( "Swap the fraction factors:\r\n" );
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document.write( "                      = \"%28+Sin%28x%29%2F1+%29%2A%28Cos%28x%29%2F1%2BCos%5E2x%2FSin%28x%29+%29\"                   \r\n" );
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document.write( " \r\n" );
document.write( "Distribute:\r\n" );
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document.write( "                      =  \r\n" );
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document.write( "                      = \r\n" );
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document.write( "                      = \"Sin%28x%29Cos%28x%29%2BCos%5E2x\"\r\n" );
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document.write( "AND \r\n" );
document.write( "\"%28Sec%28x%29-Tan%28x%29%29%5E2+%2B+%28Sec%28x%29%2BTan%28x%29%29%5E2+=+2%2B4Tan%5E2x\"\r\n" );
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document.write( "Work with the left side. \r\n" );
document.write( "Square out the two \r\n" );
document.write( "binomials:\r\n" );
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document.write( "\"%28Sec%28x%29-Tan%28x%29%29%5E2+%2B+%28Sec%28x%29%2BTan%28x%29%29%5E2\" =\r\n" );
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document.write( " \r\n" );
document.write( "\"2Sec%5E2x+%2B+2Tan%5E2x\"\r\n" );
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document.write( "Use the identity \"1%2BTan%5E2alpha=Sec%5E2alpha\" and\r\n" );
document.write( "replace \"Sec%5E2x\" by \"%281%2BTan%5E2x%29\"\r\n" );
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document.write( "\"+2%281%2BTan%5E2x%29+%2B+2Tan%5E2x\"\r\n" );
document.write( "\r\n" );
document.write( "Distribute:\r\n" );
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document.write( "\"+2%2B2Tan%5E2x%2B2Tan%5E2x+\"\r\n" );
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document.write( "Combine like terms:\r\n" );
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document.write( "\"2%2B4Tan%5E2x\"\r\n" );
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document.write( "Edwin
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