document.write( "Question 924923: (sec(x)-cos(x))(csc(x)-sin(x))=tan(x)/1+tan^2(x) please prove the identity,. do only one side please & thank you! \n" ); document.write( "
Algebra.Com's Answer #561196 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"%28sec%28x%29%5E%22%22-cos%28x%29%29%28csc%28x%29%5E%22%22-sin%28x%29%29\"\r\n" );
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document.write( "\"sec%28x%29csc%28x%29-sec%28x%29sin%28x%29-cos%28x%29csc%28x%29%2Bcos%28x%29sin%28x%29\"\r\n" );
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document.write( "Get LCD:\r\n" );
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document.write( "\"%281-1%2Bcos%5E2%28x%29sin%5E2%28x%29%29%2F%28cos%28x%29sin%28x%29%29\"\r\n" );
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document.write( "\"%28cos%5E2%28x%29sin%5E2%28x%29%29%2F%28cos%28x%29sin%28x%29%29\"\r\n" );
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document.write( "\"cos%28x%29sin%28x%29\"\r\n" );
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document.write( "That is as simplified as we can get it, although\r\n" );
document.write( "it does not look like the other side.\r\n" );
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document.write( "Even though you said to work with only one side of \r\n" );
document.write( "the identity, when we have simplified one side as \r\n" );
document.write( "much as possible and it still is not exactly like \r\n" );
document.write( "the other side, it is perfectly OK to then work \r\n" );
document.write( "with the other side to see if we can get it to \r\n" );
document.write( "this same simplified form.  So we will see if\r\n" );
document.write( "we can get the other side to \"cos%28x%29sin%28x%29\".\r\n" );
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document.write( "\"tan%28x%29%2F%281%2Btan%5E2%28x%29%29\"\r\n" );
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document.write( "\"tan%28x%29%2Fsec%5E2%28x%29\"\r\n" );
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document.write( "\"tan%28x%29\"\"%22%F7%22\"\"sec%5E2%28x%29\"\r\n" );
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document.write( "\"sin%28x%29%2Fcos%28x%29\"\"%22%F7%22\"\"1%2Fcos%5E2%28x%29\"\r\n" );
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document.write( "\"sin%28x%29%2Fcos%28x%29\"\"%22%D7%22\"\"cos%5E2%28x%29%2F1\"\r\n" );
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document.write( "\"sin%28x%29cos%28x%29\"\r\n" );
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document.write( "\"cos%28x%29sin%28x%29\"\r\n" );
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document.write( "So we were able to get it to the same simplified\r\n" );
document.write( "form.\r\n" );
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document.write( "In case you think this is a violation of\r\n" );
document.write( "working with only one side, I'll be glad to\r\n" );
document.write( "show that why it is not.  It is because those\r\n" );
document.write( "last steps can be reversed and tacked onto\r\n" );
document.write( "the first part and only the left side will\r\n" );
document.write( "have been worked with.\r\n" );
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document.write( "Let me know if you are not satisfied with\r\n" );
document.write( "working with only one side AT A TIME! \r\n" );
document.write( "I'll reverse those last steps and then you'll\r\n" );
document.write( "see that it will be the same as only working \r\n" );
document.write( "with one side.  Your teacher should have \r\n" );
document.write( "pointed this out to you.\r\n" );
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document.write( "Edwin
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