document.write( "Question 84048: using trigonometric identities to simplify the expression (csc theta)(sec theta - cos theta) \n" ); document.write( "
Algebra.Com's Answer #60514 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
using trigonometric identities to simplify the expression\r
\n" ); document.write( "\n" ); document.write( "cscqsecq - cosq
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document.write( "Are you sure you copied it right? Are you sure it wasn't\r\n" );
document.write( "supposed to be \r\n" );
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document.write( "cscqsecq - cotq  ??\r\n" );
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document.write( "I'm going to assume it was supposed to be \"cotq\"\r\n" );
document.write( "and not \"cosq\"; for otherwise it won't simplify at all!\r\n" );
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document.write( "cscqsecq - cotq\r\n" );
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document.write( "               1                1                cosq\r\n" );
document.write( "Since cscq = ------ , secq = ------, and cotq = ------\r\n" );
document.write( "              sinq            cosq               sinq\r\n" );
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document.write( "   1      1      cosq\r\n" );
document.write( "------·------ - ------\r\n" );
document.write( " sinq   cosq     sinq\r\n" );
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document.write( "     1        cosq  \r\n" );
document.write( "---------- - ------\r\n" );
document.write( " sinqcosq     sinq\r\n" );
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document.write( "Get an LCD of sinqcosq. Multiply the second\r\n" );
document.write( "fraction top and bottom by cosq \r\n" );
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document.write( "     1        cosq(cosq)  \r\n" );
document.write( "---------- - ---------------\r\n" );
document.write( " sinqcosq     sinq(cosq)\r\n" );
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document.write( "     1        cos2q  \r\n" );
document.write( "---------- - -----------\r\n" );
document.write( " sinqcosq     sinqcosq\r\n" );
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document.write( "Combine numerators over LCD:\r\n" );
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document.write( " 1 - cos2q  \r\n" );
document.write( "------------\r\n" );
document.write( "  sinqcosq \r\n" );
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document.write( "Now since sin2q + cos2q = 1, then 1 - cos2q = sin2q,\r\n" );
document.write( "so the numerator is just sin2q\r\n" );
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document.write( "  sin2q\r\n" );
document.write( "----------\r\n" );
document.write( " sinqcosq\r\n" );
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document.write( "Then we can cancel the sinq in the\r\n" );
document.write( "bottom into the sin2q in the top \r\n" );
document.write( "  \r\n" );
document.write( "  sinq\r\n" );
document.write( "  sin2q\r\n" );
document.write( "----------\r\n" );
document.write( " sinqcosq\r\n" );
document.write( "  1\r\n" );
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document.write( "Then all that's left is\r\n" );
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document.write( " sinq\r\n" );
document.write( "------  \r\n" );
document.write( " cosq\r\n" );
document.write( "                  sinq \r\n" );
document.write( "and since tanq = ------\r\n" );
document.write( "                  cosq\r\n" );
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document.write( "The final answer is\r\n" );
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document.write( "tanq\r\n" );
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document.write( "Edwin

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